Teaching

• Snape got the DADA teaching job after 15years of waiting!
• It's Snape's favourite subject
• The position may or may not be cursed.
• He made a speech to his class about his expectations once again and how he considers the Dark Arts: like an hydra.  
• He also focused a lot on defence and the need to not allow your opponent to anticipate your moves.

Since it's supposedly cursed by none other than Voldemort, it could explain why Dumbledore never wanted to give it to Snape, though it is far-fetched. I don't believe it truly is because Albus would not have trusted the job to Lupin if he had believed that even though no one was able to teach for more than one year since Voldemort was refused the position. If there was a curse, then Voldemort would have lifted it now that his most precious spy was teaching the subject!

Like I envisioned, his DADA class was through, effective and bound to prepare his pupils for what they would face. Also, he focused a lot on the essential ways to defend oneself. He also gave a speech: he always shows his intent and how he will get there to his students. He informs them of what he thinks of his subject and what he expects of them and why they should take it seriously.  It seems part of his teaching style.  

Spying

• Snape told both his 'masters' that he was spying for their respective cause.
• Dumbledore trusts Snape with his life
• Voldemort seems to trust Snape much, though surely not with his life, that would be non-canon!
• Other Death Eaters are talking in his back, one of whom is Bellatrix whose been allowed to tell what Snape told her in chapter 2 to any DE to prove his good will.
• Many people always doubted Snape for being a turncoat.
• Some people (especially Order members) trusted Snape because Dumbledore trusted him all the way. (I doubt anyone trusts him anymore however : (  

To be evil or not to be, that is the question!   Below you'll see what Jo says about it. Of course she won't spoil the surprise for us so we'll never know for sure until book7.  A shame!  However, that doesn't stop us from making theories using the facts we were provided and the loose plot elements of the books!  I sure intend to use them a lot!

Anyhow, here are ALL the possible outcomes. I'm not saying all are very reasonable, but all are POSSIBLE.

1. Snape infiltrated the Death Eater from the start and never ceased doing so.
2. Snape was forced to join the DE but arranged to get out of this tight spot thanks to Albus to whom he remained faithful
3. Snape turned his back on the Dark completely 16 years ago and is very faithful to the Light. He joined willingly the first time, but he has acted with his fellow DE to retain his value as a spy. (My shipper!)
4. Snape joined willingly, turned his back on it 15years ago, but went back to his old master at the end of Book5 when Voldemort got his powers back.
5. Snape joined willingly, then joined the Light, but once again turned his back on the Light when he saw Dumbledore was to die in Book7. And only then did he switch completely
6. Snape never turned his back on the Dark and just bide his time in the meantime, waiting for another dark wizard to lead them
7. Snape is a free agent, he'll choose whomever wins without caring about Light or Dark.
8. Snape is a free agent, he'll choose whomever wins even though he cares for either Dark or Light. Survival is stronger.

Snape is the Half-Blood Prince

• Snape's mother was Eileen Prince (sounds dead) and was a witch. A description was also provided of her.
• Snape's father was Tobias Snape (sounds dead) and was a muggle.  
• Snape called himself the Half-Blood Prince (only by himself since nobody apparently knew)

• Snape is not a wizarding name but there may have been a long lost line somewhere because  nobody seemed to mind in Slytherin. And we know Slytherins know their origins pretty well!  Maybe they thought it was some long lost name or unknown family.  

• Snape is the second half-blood Slytherin since Voldemort of whom one parent is a muggle and not a muggle-born witch or wizard
• Snape, under his nickname, helped Harry tremendously throughout the year in Potions. Irony at its best ^_^

I admit this was a surprise because I thought the 'prince' would be a new ally.  I'm very glad this brought about so many answers about Snape.

I wonder if there's a specific meaning to Snape being the only Slytherin since Voldemort to have one completely Muggle parent?  Maybe that's again a device to make us associate Voldemort and Snape together and think they're both evil since they have a similar history. However, this is very misleading in the book because it's spoken from Harry's point of view. He's the one making the correlation between both and it's very misleading to believe what he says. For example,  I don't believe in what Harry said about Snape wanting a terrific name like Lord Voldemort however. No, or else people would have known about it! Yet nobody did! And in this era of Internet nicknames, who never wished for a cool grandiose one?!  I sure did when I was a teenager though I never had delusions of grandeur ; )

Maybe his self-conceived title was a way for Snape to dissociate himself from his family name. Maybe he was very shy and/or ashamed of his father, especially since the only glimpse of him we've had was him frightening his wife and baby!  Hence, it would be natural for him to want to change his name to his mother's.  

Potions

• Snape was a genius at Potions since he was able to make his own potions or change any existing ones
• Snape added his notes to his mother's book, therefore, she may not be the one to have instructed Snape on the subject.
• He can thus invent new potions, he's not merely emulating everything from a book. That's surely something that tickles Snape about Hermione: she's good, but she won't go farther than what's written in the book. No wonder he calls her a know-it-all. It's not like she ever came up with a modified potion like he did! And also, no wonder Hermione is jealous of the HBPrince for being so clever ^_^

Indeed, for someone to rewrite an entire advanced Potions book on his own, he must have been a 'genius' at it. No wonder Dumbledore gave him the job when he was only about 21!  Do you think he showed him his notes though? Maybe not, so either Dumbledore knew of Snape' spectacular talents beforehand or he demonstrated on the spot his skills.  I am more found of the first option because Dumbledore told Snape he'd see how he'd fare in Potions, he never said he had tested him.

The Potions book

• Snape left his Potions book in his old classroom.
• That book was his mother's because of the edition date, around 1950 (if I remember right).
• Either his mother or him were not very careful of their books. I would say Severus would not be with a book he had to rewrite because the potions were not top notch. He wouldn't mind doing that to a book he believed was lacking in flair!  Note that we never heard of his other books as looking like that (enough to give Mrs Pince an attack), so I would say age, his mother and his handling of the book rendered it like that.
• It points at the fact that Snape could, if he wanted to, publish books and take Potion making to new heights!  I wish he would! But maybe wizards don't like new books and prefer old recipes

Snape finding out Harry has the book

• The fact that when  Snape  told Harry that he would not allow the boy to use his own spell on him, and annoucing that  he was the HBP, proves that in the bathroom, even though Harry had just brought in a false copy, Snape knew of Harry's possessing his book.  
• And he confirmed it the same day, surely by visiting the place where it should have been  in the Potions classroom where he found a new book with an old cover.

What is unclear is why he would leave the book there. However, I can think of those reasons:

• After 15 years of Potions teaching, surely not a single student ever dare ask him if he 'had a copy to spare'.  That would be a laugh! So maybe he simply forgot it was there
• If he was always such a genius at Potions, surely he doesn't need the book and hasn't for years now.  Hence, another reason for forgetting it was lying there. It was not a Journal after all.
• Rowling needed Harry to have that book! Ha ha! Yes, the laws of plot development were at work here ; )
• It also points at his never publishing a revised version of this book and I think that's a real shame!

 -It was easy to connect the dots when he discovered Harry had used his Dark spell in the bathroom: Harry being excellent at Potions (more than Hermione) + using Sectumsempra when Snape was aware it was the first time for Harry to use Dark magic + Harry not knowing what the spell did (having found it in a book) = Legilimens!  Snape used Legilimens the second he suspected Harry to confirm his suspicions.   

Charms and DADA

• Snape was so proficient at Charms and DADA that he was able to create his own spells.
• He seems to have written them into his Advanced Potion Making book.
• He developed some Dark Magical curses, too.

I thought it was so great for him to invent spells. He may have written some more in other books though. Wherever he wrote them down, they were new spells and therefore worth respect for his skills.  It seemed almost a way to pass time and plot his revenge at the same time. Also, Snape's Worst Memory (OP 28) comes to mind because one of the spells he invented was used by James on him.  And how much he must have been enraged at being thrown in the air by his own spell!  It would also confirm that Snape tried his best to retaliate and defend himself.  Also, his spells were useful to spy or hide something.

Snape's home

• Snape spent his summer away from Hogwarts.
• He lived down in Spinner's End in a ragged 'Muggle-rat hole' kind of accommodation.  
• It is full of books.
• Wormtail was sent there to assist Snape (there doesn't seem to be any house-elf there) and possibly spy on him
• The house is his but was described as not usually inhabited.

What it may look like (thanks to Afictionado for these explanations and pictures! Click on the titles):

Slums 1
How’s this for a Muggle dung hole?  Not bad, I think – the bricked up windows make the houses look extra grim.  And these are flat-fronted houses so very probably their front doors open directly into the main rooms.

Slums 2
Not quite right – the gardens threaten to make it too pretty, and the trees behind make it look slightly rural, as if it’s on the edge of town; but I decided to let you see this as well as the first picture.  I suspect that originally these houses were built without porches, and those that have them have added them later in a bid to get rid of the front door opening straight into the main room.

Slums 3
This shows a cobbled street in the centre of a town, so the street is lined with shops and business premises rather than residential housing.  I know it doesn’t show a Muggle rat hole of slum housing, but I love the wet roads and pavement that look almost greasy.

May or may not be a habit of his to spend his summers out of Hogwarts.  

If this was his 'home' once, someone like Snape would surely not like spending his time there each year!  The house seems very hard to find however, which is why he may have chosen it since the return of the Dark Lord and so he could 'entertain' different kind of guests. Narcissa knew where to find him however, so maybe it was his home a long time ago, before Hogwarts.

I think it was his home once but ever since it was left to decay. Since when exactly, we don't know. This may be the place he was shooting down flies from, but since it's in a Muggle neighbourhood, I find it hard to believe unless there were no one else around. Maybe he was allowed magic inside his home.  As we learnt, the Ministry cannot identify who does the magic inside one home.

Snape towards the DE and Voldemort

• Snape is now the most trusted of the Death Eaters because he is the best spy Voldemort could get.
• Snape rejoined the Death Eaters two hours after the initial call. Maybe Voldemort intended to kill him for not coming back as mentioned in Book5, but with his excuses, Voldemort forgave him and took him back within his ranks.
• Narcissa says the Dark Lord trusts Snape
• Wormtail spies on Snape, but the latter treats him with contempt.
• Snape took up the post upon the Dark Lord's orders (that's his DE version to Narcissa)
• Mentions that he thought the LV was dead and that's why he didn't seek him out like all the others.
• LV is pleased Snape never left Hogwarts and has 16years of info for him
• Snape considered his job 'comfortable' and it kept him out of jail thanks to Albus
• Snape defended the Philosopher's Stone because he was protecting it from Quirrell, LV didn't show himself since he was afraid Snape would betray him then.
• Snape was asked to remain behind while they attacked the Ministry in Book5 (from his DE side)
• Snape is not the secret keeper of Grimmauld Place. (However, how come Harry can speak about it so freely then?!)
• Snape participated in the capture and death of Emmeline Vance
• Snape said he had kept Harry alive because only Dumbledore was keeping him out of Azkaban and killing the boy would have been too suspicious.
• Snape considers himself a great actor (DE part)

The Slytherins, the office and Snape's quarters

• Snape kept his office in the dungeons while his classroom is now upstairs in the DADA classroom. His office seems unchanged. He may still brew many potions there.
• Maybe Snape kept his quarters, too.  JKR didn't mention Slughorn lived in Snape's old quarters, and the dungeons must be large enough for everybody.
• Snape's personal belongings will be taken care of by someone of the Order in Book7, I believe, or by the Aurors.  But I highly doubt they'll find anything incriminating. Snape was very cautious all the time!

 I believe Snape kept his office there in order to cover as much of Hogwarts as possible easily and without anyone suspecting him for being where he shouldn't be.

He's also near his Slytherins in case of trouble. That's why I believe his quarters are still in the same place.  

Mad-Eye Moody never found anything Dark in Snape's office or quarters, so that's proof enough they won't find anything after his departure from the castle.