Hm, all of things I ship are from the games, since I'm not too familiar with the other canons.
Most of my shippings are from the Hoenn games--May/Wally, May/Brendan, and Steven/Wallace are the ones I like the most. I tended to make up scenarios in my head as I played, like May having a crush on Steven but he's really in a relationship with his best friend, Wallace. I mean, what's the fun in shipping if you don't have a story to go with it, right? ^_^
Interestingly, that was the first time I really stared shipping... at all. My first same-sex ship ever was actually Archie/Maxie, a pairing that recently got really popular, like, on tumblr in the fandom. But I've been shipping it for years! :3c
To a lesser extent, I ship Giovanni/Ariana (but I see them as having had a really bad falling out).
EDIT: Oh, and how could I forget the moe moe Serena/Shauna (I see Serena as the protagonist)! I wish I shipped more girl/girl pairings from these games....