A tricky element to bring into any games depending on the maturity level the players involved. A lot of times groups just avoid the subject all together to avoid any issues at the table. I personally have discovered that it's fine to introduce it, but try to keep it away from PC to PC relationships (unless they invite it.) and generally play it at about the Daytime TV drama level.
Now if you'd like to sneak it into a game with out freaking out your players I have discovered a few tricks.
The "Rival" -
Nothing breeds romantic tension like a semi-hostile npc that pops in, flirts with their rival PC and then darts out never playing through the relationship until you get a feel for the group that it's something that might happen. This keeps the PC's from feeling too weird at the attachment. The 'oh, it's them' feeling allows for banter in full Moonlighting style. If the PC doesn't seem interested, have the rival move on or fall to some mysterious fate and you are done. I've had good use of this in Exalted. In a high powered, big ego game like that a powerful romantic rival is perfect to draw out the PC's acting skills. At least it gives them someone interesting to use their social combat skills on.
The "Offer" -
This one is useful and dangerous. The way it happens is the relationship is a set up between an NPC and the PCs for some poltical or criminal reasons. It could be an offical 'marry the dutchess to gain access to the castle" or more casual "help my friends and I by joining our family". I'm going to give you a few cases of this just so you follow what I'm talking about:
1. The party was dealing with a powerful witch coven needing aid against a squad of werecreatures. The Green Hag wanted to extend her coven but didn't want to allow too much inbreeding among her followers. So she...*ahem* seduced the drunken monk of the party one night while they were negotiating for help. He went along with it because, she looked nice at the time and hell 'drunken monk'. The player thought it was funny he now had a Hag girlfriend and then I told him he would most likely have a daughter by her. (A lot of the reason why the Hag helped them is because the Monk played into her plans.) The player went 'cool!' and asked to play his daughter if we ever picked the game back up again.
2. Another PC arrangements this time was a group who was looking for support against a powerful rival faction at their school. Well in traditional Ninja High School fashion, the marriage of 'clans' would suffice. Hilarity ensued.
The "Danger" -
If you have an amorous player looking for NPCs to add to his or her little black book I have a technique to add a potential romantic interest that eventually betrays the party. Mind you, the person still feels conflicted about their choice and sometimes gives clues and hints to help them. Not a pure betrayal, but more a holding to their prior oaths issue. It's great for drama.
In this case I had a party Paladin Half Orc fall for a hot Elf Druid. Only she belonged to a sect of murderous 'fire' druids that sought to purge and change the world in turn helping a group of Were monsters. Yes this was the same game as the drunken monk/hag relationship. Needless to say the relationship drama added punch to the plot.
The "Student" -
Not my idea, but another player in a group took a 'maid' under his care in an Exalted game, awoke her essence and then proceeded to romance her keep her around as his personal assistant and pupil. I've seen this happen a lot to "pet" mortals in Exalted games. Romance them, equip them, turn your servants into lovers and living weapons. It's quite...different.
The "Casual" -
A romance interest with out emotional baggage who is just part of the character's background. Someone they spend time with between missions and the player is allowed to flesh out what happens at their leisure. Just like some relationships are low stress and fun to toy with, these are great. It helps if the NPC acts as an asset either with information or perhaps acting as a gofer or party backup for less dangerous needs.
Notice something, none of them are the "Damsel". While that type of possible romance exists it's also a: played way to often and b: less fun for the players. Damsels are rarely helpful to an adventuring party and often squick out potential female players. Unless the Damsel is a guy...and well, playing against norms is fun here and there.
However you slice into the romance pie though, make sure the players are on board with you. Or, well. It could get messy.