Romance in a game can be tricky, tacky, gross (as in cheap 70's porn-style discription), or something absolutely unique and memorable.
In my Conan game, I had three players. Two males, one female. The female had a female PC, and I had several NPCs (including one specific male NPC). When these two met, it was almost a blood-bath. And, as games progressed, they grew attached to each other, found out just how similar they were, and it was something that was absolutely beautiful to both witness and participate in. It was just the right quantity, and just the right time... Between savage sword battles and all (it WAS a Conan RPG, you know).
But, for that one unique "relationship"... There were dozens of other games (in which I was a player, not the DM) in which the romance was tacky, cheap, and forced. Females wanted to be with males, and vice versa. No real reason, no real long-term goal. Print a picture online, use that to describe whatever NPC of the moment, "oh hey that's hot, I'd hit that", describe cheesy and slightly gross making out session, they're an item, and that's that.
Cheap, ineffective, and lazy DMing.
Between players, it needs to be either mature players that are willing to take a second to think about how their PC would react, or people that know each other well enough to play the "romance" game out, even if it turns out to be a disaster.