Some readers love them, some readers hate them. Entire books have been built around them, and fans will practically go to war to defend their particular choice. They're love triangles, and they're a bear to write. Before you do it, find out if it's even worth it to include this very dicey plot point in your story.
Three's a Crowd
She likes him, but he likes someone else. It's a classic scenario, a literary tactic so old you can even find it in Shakespeare. Or maybe even in the Bible. And because it's so old, it's going to be really hard for any writer to use successfully. Readers have already seen it all before.
That's why you have to make you love triangles fresh and interesting if you're going to include them. Shakespeare didn't stop at a three-way knot of emotion; he added more parties to his triangles. While Helena was pining for Demetrius and he was pining for Hermia, she was madly in love with Lysander and all but oblivious to Demetrius. Then, a fairy gets involved and starts making all the wrong people fall in love with each other. Doesn't that sound good? Isn't that something you'd like to read?
It was popular 400 years ago. So if you're going to add a love triangle to your plot, you're going to have to really mix it up. Stephenie Meyer made it work by creating a love triangle out of three different species of humanoids. What's your gimmick?
You can always add fuel to the love triangle fire by adding more parties. Why stop at three? Add more love interests, more confusion, and foil the couple that "should be" together time and time again to keep readers interested. If you do it well, you can build suspense without breaking their patience. It's a fine line to write, so have a care. You can make your love triangle more engaging by dramatically changing someone's social status (a very wealthy love interest suddenly loses their fortune, for example), or putting one in a life-threatening situation to test the main character's loyalties. Perhaps the main character's parents hate one of the love interests. Mix it up, change it around, and make the plot unique. It has to be different if it's going to work.
The Sticking Point
Writing a juicy love triangle that's filled with suspense can be done with a lot of hard work. In order to resolve the damn thing, you're going to need luck and a whole lot of imagination. At some point, the story has got to come to an end. A choice must be made. So who will it be? And what's going to happen to the other one?
Resolving a love triangle is incredibly difficult, and some writers will come up with truly wild and crazy ways to put a cap at the end of theirs. You can't just show the happy couple riding off into the sunset; readers are going to demand to know what happens to the one who's left behind. Does the rejected love interest find a new love? Do they decide to leave the area instead, maybe explore the world or try some new career? In some books, the spare lover might die. That's a resolution, too.
Whatever you do, find your resolution and put a decisive end to your love triangles when the time comes. There can be no loose ends where matters of the heart are concerned. At some point, the sequels have to end and the matter has to be resolved.