Let me tell you a little story...
Picture a teenaged boy, not the best academically, but not poor. Not the most attractive either, but a good amount of girls have a crush on him anyway, some due to the fact that he is good at sports. Rather cruddy home life, with two best friends, one girl and one guy, the girl being bookish and the boy being a bit of a slob.
This boy has a massive crush on a girl with long black hair who is also good at sports and is a year older. He harbors this crush for quite a while, going as far as to ask her out to a dance, but she says no.
They finally, FINALLY get into a relationship, but it goes very badly, what with her being hung up on another guy and crying all the time. The relationship crumbles and he realizes that she is kind of annoying and cries WAY too much.
He spends the summer with his friends and meets Girl #2. #2 is sporty, smart, witty, and beautiful. As they hang out more, they become closer and closer, but she has a boyfriend, who is a friend of the boy's, but that relationship has been going a bit downhill as of late. He even sees them together often, and realizes he is jealous. They break up and one day, he works up the courage to kiss her and they start going out.
Know who it's about?
Because if you guessed Harry, Cho, and Ginny, you are 100% WRONG. That was about my best friend Andrew, a girl named Idalis, and a girl named Cece.
A similiar relationship happened to me, with two boys named Ben (Ben being Cho, although his problem was that he showed NO emotion, instead of way too much) and a boy named Francis.
The whole point is that a Harry/Ginny relationship is not all that uncommon. Besides, really think about it. Ginny was completely off limits, as she was Ron's sister and besides that, he was hung up on Cho. Of course Ginny wouldn't show she was jealous of his relationship with Harry because I'm sure she didn't see the point of pining over someone she feared would never return her feelings, and I'm sure we've all felt THAT one before! Besides, Harry hadn't really spent that much time with Ginny before, so when he went to the Burrow early, he got a lot of extra time with her and saw that they seemed to have a lot in common and started to develop a crush on her, which led to love.
Then there's also the fact that Ginny seems to bear a lot of resemblance to Lily, and we all know Harry is a good amount like James. His marrying Ginny is not due to any Oedipal Complex, like others have brought up. It is a proven fact that most people will marry someone who is similiar to one of their parents. Many girls marry men who are a lot like their fathers, and many boys marry women who resemble their mothers. It's not weird, it's normal.
The relationship is also anything but random and weird, as I pointed out with the story of Andrew. There is also the fact that Ginny has cheered him up in the past (the chocolate eggs for Easter in OOTP) and he doesn't just all of a sudden get jealous when he sees her with Dean. He expresses some sorrow when she leaves to sit with Dean on the train, smells a "something flowery that he might have smelt at the Burrow", talks to Ginny, a lot, and a few others I may have missed, and THEN he gets jealous over seeing them snogging. He also thinks about her a lot for the rest of the book, being confused by his feelings, getting goosebumps when she plucks a maggot out of his hair that "had nothing to do with the maggot", feeling like a jerk for forgetting that she was possessed, feeling complete elation when she breaks up with Dean, and THEN he kisses her.
Oh yes, that was a completely random kiss right there, just out of the blue (sorry, couldn't resist the sarcasm).
If one is going to use "textual evidence" and "real life examples" to disprove Harry and Ginny, I would suggest re-reading the book and asking actual people before making such assumption.