Okay, I sincerely doubt I'm going to come up with anything about 30 people haven't mentioned already but still, you asked why I support a Harry/Hermione ship and I'll give them.
Books

Most of my majors comes from GoF mind you and a lot of it just suggests that Hermione likes Harry since Harry is still all about Cho in the 4th book (cross fingers on that changing

)
Long walks around the lake, attending classes together, all that spare time without Ron...
She didn't seem to mind all that much when everyone was teasing her about dating Harry after Skeeter's article
Hermione was praising Harry up and down after the 2nd task even though KRUM SAVED HER.
The fact she won't stop talking about Harry to Krum (it must have been a lot for Krum to threatened)
The kiss at the end.
Movies
Most of my cannon evidence for the possibility of a ship comes from CoS. The second time I saw the movie (because I was completely dumbstruck with awe the first time) I noticed that when Harry and Hermione ran into one another at Diagon Alley she was totally checking him out after she finished fixing his glasses. She looks him up and down like he was a hunk of honeydukes chocolate and she wanted a bite
And then there's just the hand holding and flower bringage when she's petrified and the big ol running towards one another with open arms hug in front of the whole school thing.

Not to mention the "well we had loads of help from you" comment just oozed affection.
Okay, I'm done because I know I'm going to be very bummed if Harry and Hermione don't hook up in the books (but I'd like to think that JKR wouldn't let Chris Columbus take such liberties in laying the groundwork in the films for it later on if she didn't intend for it to happen eventually).
Well, I'm off an running,
Oy! Angie