This set of recommendations is for what I consider classic Snape fiction.
I started reading the Harry Potter books after the second one because I wanted to be able to discuss with my nieces something they were so excited about. My take was a little different, though, because I was a Snape fan from reading the first book. ;-) I stumbled into fandom shortly before Order of the Phoenix when a friend mentioned fanfiction.net. And from the first, I loved the Snape stories that portrayed him just as I read him: a damaged but essentially good (although decidedly not "nice") man just trying to do the best he could, struggling to teach kids who thought his subject was stupid, dealing with stupid bureaucracies, totally pants at interpersonal relations and work politics, and getting no credit for it when he managed to get it right. These stories were all started pre-HBP and run the gamut from Snarry to gen to Snape/OFC. One of my faves pairs him with an OFC fighting against the memory of his idealized Lily, on whom he has a massive crush. So, anyway...
The Birthday Present, by excessivelyperky. An alternative to Half Blood Prince, begun before that book was published, and portraying Snape as a poor pureblood with a very nasty family background, struggling with all his might to do the right thing despite facing increasing hostility from some members of the Order and the thought that the ones he was betraying actually value him more than the Gryffindor Order of the Phoenix. That summary does not do the story justice, really. It is one of the few stories I have ever read that is very sympathetic to Snape (sometimes a tad too much so), yet shows Harry Potter struggling with his own demons and growing into a responsible adult, while at the same time fleshing out the "minor" characters at Hogwarts and making them into real people. Anyone who thinks Flitwick must have an interesting backstory will love his parts in this.
A Nick in Time and its sequel,
Growing Pains, by Tira Nog. Classics in their genre.
A Nick in Time is the story of a deaged Severus and Harry, who learn about each other and what it is like to have a family. The sequel is a Snarry which builds on the first. I can't say enough about these. Severus is nominally a pureblood (muggle-born father) orphan raised by his pureblood fanatic grandparents. Absolutely superb.
A Memory Found , by Mystical Dragon. Severus is tortured with the Cruciatus curse to the point where childhood memory charms begin to crack. Begun in 2001 and, reading through it now, it's clearly written early in fandom and is rough and a little fantastical in places, especially as the story progresses. But it deserves credit for being one of the early stories to tackle head on the pro-Gryffindor/anti-Slytherin state of Hogwarts under Dumbledore, and having Harry's eyes opened to its effects.
A Gift of Light, and its sequel,
Loving Bonds, by Josan. Snape/OMC. Severus discovers he has a son from a short fling with a woman, and the fallout. He grows in ways unexpected, especially to himself, and the resulting devotion to his son creates a rift with Dumbledore. I can't say more without giving away the twist in the plot, but this is a fantastic story. It's also the one of the two (along with
Growing Pains) to convince me that for some reason, Snape slash seems better at developing Severus as a real character, as opposed to a caricature of the "mean teacher who exists to show that Harry and his friends are pluckily undaunted by the establishment."
The Smallest Slytherin and
An Obedient House , both by Rebecca Webb. Predate Order of the Phoenix. Sometimes a bit over the top, but an interesting look at Severus as the Slytherin housemaster.
Squidbait Returns, by Grainne. This is just
fun! Yes, it's Snape/OFC and the OFC is the new Defense against the Dark Arts teacher. But it's an OFC like you don't normally see (just one hint: she was known as Squidbait at school because she fell out of the boat crossing the lake, and the Squid spit her back). Briefly, she was a little behind Severus at Hogwarts and had a massive crush on him as a teenager, while being entirely (and painfully) aware that Severus had a massive crush on Lily. It contains one of the funniest, non-idealized, yet ultimately satisfying sex scenes I've ever read.
Brave New World and its prequel, The Potion Master's Life , by theatresm.
Brave New World is a satisfying Snape/OFC story, while
The Potion Master's Life is a poignant and utterly unique look at Severus' childhood. As an aside, does anyone know what happened to theatresm? Her LJ has been purged, and I fret that these may be taken down as well.