I'm only going strictly from the anime (as I don't play any of the games anymore. Gen. 1)
I dunno; I just think cavaliershipping is underrated. To be honest, I can't see anyone else other than Ash (or a little bit Barry, hetero speaking) with Dawn. Gary will always be one step ahead of Ash (or better than him depending on who you ask, lol), and with the episode that Gary and Dawn met, it was cute. If anyone could make Ash jealous (in any way, not just in a romantic way), it's Gary.
I also don't know why, but I like rayshipping a lot as well. Tough to explain why. I guess they embody the whole pokemon concept of training and friends.
Kind of a crack pairing (don't know the name), Ash/Elesa intrigues me. I saw the BW episode and laughed when I thought of Brock's reaction to her jumping down to see Ash's Pikachu. Prolly the electric pairing.