Out of all the potential couples listed in this thread, I feel like by far Garen and Katarina is the pairing that contributes the most to the character development of the two champions in question.
I'm not really one for things romantic, and usually don't get into this whole "shipping" buisness, but I make an exception here just because it gives such a fantastic opportunity to examine the similarities and differences between the philosophies behind Demacia and Noxus and the conflicting elements of human nature that form their basis.
...Geez, that's a really... clinical response for such a thread. Heh. Don't say I didn't warn you.