Besides the real life romance of two members of our gaming circle who met in one of my games and are now married, we've frequently had romance, both between PCs and between PC & NPC. (I know, Stormborn will say this plays into every stereotype about female gamers, but--) The two of us females in the group usually come up with some complicated backstory between our characters, and what better to complicate PCs lives than romance?
One of the funniest/weirdest was in a Call of Cthulhu campaign run by my husband. I was actually playing a female PC (for once), Nia, who had a crush on Kent, a university colleague. Following a particularly intense event (and what, in CoC, isn't?), the two sought solace in each other's arms. And since the GM is evil, Nia got pregant. When Danny (the other female player) found out (he tended to be protective of Nia), he hauled off and punched Kent right in the nose. Absolutely hysterical. Shocked the player it happened to, I think. One of our favorite gaming moments.
And there's Stormborn's homebrew Leviathan game with a complicated love triangle. Raef was in love with Ari who thought they were only friends. Then they meet Will (NPC), who was intended to be a minor plot device, and Ari falls in love with him. Needless to say, Will is still in the game and Raef's heart has been broken. He's a bard though, he'll get over it.
I say, what's roleplaying without romance?