I think it really depends on what kind of story you're trying to tell. I think the real key is whether your game is character driven or plot driven. Character driven games are usually going to fare better in the romance department.
FFIX had a couple of fantastic, low-key romances. A big part of why they worked was because of how character-focused that game was. The main plot was sometimes driven by an external force, but most of it was driven by your party members. You were always, always thinking about who the characters were. Every quest had you learning something more about your companions. It's very natural for a game that's character driven to have a focus on the character's relationships with each other; and as other people have pointed out, romance happens when you save the world together. FFIX had no problem showing us the chemistry between characters, and the way they "acted differently" around each other, because half of the damn game was watching your party talk to each other. It was easy to tell that Zidane treated Garnet pretty differently than he treated Freya.
FFIV is another example of character-driven romance. Here, the plot is more external, but the game compensates by having the main romance (actually love-triangle) be already established at the start of the game (so it doesn't need to develop from scratch). It also uses the romance as fuel for conflict (see: Everything Kain does in the entire plot), without turning it into Romeo and Juliet. (It's easy to kidnap the hero's girlfriend and use that as motivation to kill the villain. It's a lot more interesting to have the Kain angle added in.)
Then we get FFVII. Ah, Cloud and Aerith. To be honest, I never gave a single frick about them. I felt it was a really forced romance. Why? Because, honestly, Cloud and Aerith didn't fall in love for character reasons. They fell in love for plot reasons. The plot demanded a dead girlfriend to fuel Cloud's wrath. Then they threw in some stuff about absorbing Zack's memories of being in love with Aerith to try to cover up the wires, but...Honestly, it just didn't work. The plot of FFVII is very external. Things don't happen because of your party members as people. Things just happen and these people just happen, for one reason or another, to get sucked into the mess. Really, Sephiroth and Cloud are the only people who drive the plot in any meaningful way. You could have replaced Aerith with Tifa no problem and the game would have continued on exactly the same. Dead girlfriend, much wrath. (Though granted, you would have to change the exact circumstances of the girlfriend death, but it wouldn't be hard to do. Have Tifa die protecting Aerith as she finishes summoning Holy and boom. Same plot.) (Not so, you'll notice, if you tried to switch out characters in their respective subplots in FFIX)
And then they came in and gave you romance options with Tifa and Yuffie and even frikken Barret and...*shakes head* It didn't kill the game, but it very well could have if there wasn't so much else going on that you could ignore the terribly-implemented romance.
Teal Deer version: I like romance when it's done well. It's a lot easier to do well in a character driven game rather than a plot driven one. That is, when the characters are the ones driving the story, rather than the story driving the characters. Also, the more we see the party interacting with each other, the easier it is to slip in a romance.