I love so many pairings in FMA... RoyxRiza, EdxWinry, RoyxEd...
If any romantic relationships happen, I think that EdxWinry is the most likely. They've just been too close for too long for nothing to happen. Winry is the closest to Ed, barring Al.
Unfortunately, while the manga hints at it (haven't seen the anime *sweatdrops*, slow connection), I don't think that anything will happen. The manga doesn't really focus on romantic stuff, so it's unlikely that they'll suddenly switch to including a romantic relationship, even a tame one, like Ed and Winry's would probably be at the start.
Also, until Ed finds the Philosopher's Stone, he's way too focussed on that. Some time after he finds the Stone, when he and Al are back to normal life (or as normal as life is for a State Alchemist

), then he might realise that there are girls in the world. Then, Winry would be prime candidate for a relationship.
Ah well, we'll just have to wait...