Okay, so there a trillion and one Harry Potter ships out there, but I'll bring you a little info on the major ones, involving Hermione.

The Good Ship - Side Kickers

The Sidekickers. Ron and Hermione shippers ship this particular ship because of the constant bickering and aruging between the two characters. This ship is also part of a bigger sub-category of OBHWF (One Big Happy Weasley Family) and relates with Harry/Ginny and Neville/Luna. Many people ship the "HeRon" ship because of the sexual current and bickering that surrounds this couple within the texts. Rowling presents the two characters are often quarrelling "like an old married couple" and throughout the series, their affections towards each other are made evident. Ron's assuming manner in 'Goblet of Fire' at Hermione being 'dateless' for the Yule Ball drives him to be jealous when it is revealed that Hermione was asked to the Yule Ball by a handsome Bulgarian National Quidditch player, Viktor Krum. Jealousy is also shown on Hermione's part in 'Half Blood Prince' when Ron becomes noticeable when he joins the Gryffindor Quidditch team - his relationship with fellow Gryffindor Lavender Brown results in much bickering and fighting.

At the conclusion of the text, Ron and Hermione marry and have two children - Rose and Hugo.

Harmony - Pumpkin Pie

The hero/heroine ship. This ship and the ship above have constant wars as to who Hermione will end up. The whole basis of this ship is that Harry and Hermione are kindred spirits - they are always together and help each other out. This relationship is of mutual understanding and respect. This relationship relates with Ron/Luna and Neville/Ginny. Shippers of the "HarMony" ship look between the lines of the relationship held by Hermione and Harry. Viewing their mutual trust and respect for one another, plus their close bond which often blurs boundaries, as a sign of devotion and affection. The series is related to us by Harry's perspective and Hermione, unlike his crushes, remains the same, with the same "bushy hair and buck teeth" (a flaw she corrects in her fourth year). While they do not bicker as their HeRon counterparts, there is suggestion by outside characters as to their relationship - it is commented upon by Cho Chang, Rita Skeeter and an assumption is made that the two share romantic interest in one another.

Harry ultimately declares his love for Hermione as "a sister, nothing more". He marries Ron's youngest sibling, Ginny Weasley, and their children James Sirius, Lily Luna and Albus Severus are cousins of Ron and Hermione's children (and are all a part of the ever growing Weasley clan).

Dramione - The Leather Library

The whole notion of love/hate. There isn't much canon proof, but there sure are some talented people out there who can make you think otherwise! This ship is one of the funniest and has the whole "house unity" and "I hate you, I love you" sense to it. A very popular ship.