I am an avid reader of HP fanfiction, particularly of Hermione-centric fics, since I simply adore Hermione as a character (with all her strengths and flaws). Luna Lovegood and Neville Longbottom make up the trio of favourites.
I do enjoy Hermione`s ruthless, vindictive and manipulative tendencies, provided they are tempered with compassion, insight and wisdom, which I thought Hermione has the immense capacity to learn and develop. My revulsion of HBP and DH (much less so, but still...) Hermione stems from the fact that no such positive growth were given to her or most other characters in the later books, hence my love for books 1-5!Hermione (which still showed the potential for positive character development) and fanon!Hermione.
Amongst the hundreds/thousands of Hermiones I have had the pleasure to read/encounter (in fanfics), the Hermione/s from Vera Rozalsky`s HP series stand alone as personal favourites, followed by BlackLotus`s Hermione in Dangerous (disclaimer: I don`t enjoy reading Dark!Hermione/s, but a Grey!Hermione is ALWAYS welcome).
Luna and Neville, on the other hand, are overlooked to a high degree in both the books and fandom, which is a sad state of affairs, given that they are the persons with the kindest and nicest personalities and characters in the HP-verse, not to mention brimming with courage as well. That said, I am happy that JKR gave Neville the character development he deserved (the one satisfaction derived from DH), and deigned not to butcher Luna as well, though her book-page time was sorely lacking.
While I don`t like Severus Snape per se, I think he is a fabulous character worthy of deep respect and gratitude. Truly, Neville and Severus are the unsung heroes of the HP world.
Canon-wise (yes, I know it didn`t happen, but that won`t change the fact that I want them to), I ship Neville/Hermione and Viktor/Hermione (Harry/Hermione as well, when the mood is more forgiving of Harry).
With the notable exception of Hermione/Ron (canon and/or fanon), I enjoy and am open to reading any and all ships (or non-ship if that is the case) with Hermione as the main protagonist. Hermione/Neville Longbottom, Hermione/Viktor Krum, Hermione/Severus Snape, Hermione/Kingsley Shacklebolt, Hermione/Lucius Malfoy, Hermione/Draco Malfoy, Hermione/Fred/George Weasley and Hermione/Any Minor Male Characters fics are particular favourites. Hermione-in-rare-pairings are of especially keen interest.
Hermione/Neville is my het OTP and Hermione/Luna is the femmeslash equivalent. ;)
Lois & Clark is another much ventured into fandom. There are times when the phanfiction world of the Phantom of the Opera beckons, with Erik/Christine a favourite therein.
Last but not least, Haruka/Michiru forever! :)