Oh, don't get me started. I'm grouping the Elite ships in here too because I love them. ^_^
Lance x Lorelei
I've been shipping these two since before I knew that what I was writing was called fanfiction, and what I was doing was called shipping. I don't remember how or why I got hooked on them, but it may have been opposites attract- Dragon x Ice. In any case, if I'm ever caught waving a little OTP flag, it's probably for these two.
Giovanni x Sabrina
I believe this is called Socioshipping and even though I don't tend to use ship names, I'll use this one because it's so awesome. I think the personalities of these two characters mesh very well and the tension between them is always fun to play with- they're both very reserved individuals who are very concerned with appearances and reputations. They are also both absorbed in their work with the Team. They need an outlet.
Karin x Clair
I do not remember how I got hooked on this one. May, again, have been a bit of opposites-attract- I always imagine Karin as being fairly outgoing, but Clair is reserved and a bit arrogant. This one has its roots in my personal fanon.
Morty x Will
First off, I'm convinced they are brothers and you will never convince me otherwise. My rationale for this one is mostly based out of my little fanon, but I think they're compatible.
Bruno x Whitney
I just think it's cute.
Wallace x Steven
Originshipping. Others have said it better than I. It's eye candy and it works and it's canon, I swear.
Kamon x Jasmine
OK, so Kamon/Silver/Black/Name-of-the-week isn't a gym leader, but he's close enough. And you can blame this site here for keeping this ship on my radar:
http://www.sun-inet.or.jp/~tukinode/blamitop.html
...nice? A Saske rip-off dating such a cute girl is NICE?
I'm sorry, did you say something? I promise you I have more experience in shipping wars than you do, and I haven't had a good one in awhile. You want to take this outside?
Tate x Liza
Because I can.
I'm waiting for more information on Hyouta and Natane before I work them into my crazy little fanon scheme, but I like them already.
I miss the Unconventional thread.