Buffy/Angel/Spike - Buffy the Vampire Slayer
This trio was legendary in many ways, one of which happened to be a love triangle. Buffy had a lot to worry about and while romance was one of those things, it wasn't even close to all of it. There was careful thought being used when approaching Buffy's connection with both characters, and there was also a nice twist where they weren't enemies. In fact, Spike went on to appear on Angel's spinoff show, a great sign that it wasn't all about a love triangle.
Klaus/Caroline/Tyler - The Vampire Diaries
There was nothing chill about these three, but this triangle always put Caroline's feelings first. She was in charge of which relationship she would or wouldn't be in. This allowed for her to make decisions she didn't feel ashamed of and that got her to a place where she knew what she wanted.
Nathan/Audrey/Duke - Haven
There may not have been many people around to witness this love triangle, but it was a joy nonetheless. Audrey may have gotten together with Nathan, but that doesn't mean that she lost her close friendship with Duke. The relationships stood out beyond who Audrey ended up with, it was about the connections that defined the show.
Hannah/Bones/Booth - Bones
Bones and Booth may have belonged together from the very beginning, but the care that was offered to Hannah shouldn't be forgotten. Even though it was a rebound relationship, Booth and Hannah were still offered a relationship journey that focused on them both. On top of that, Bones and Hannah were allowed to have a friendship that didn't cling to jealousy.
Dawson/Joey/Pacey - Dawson's Creek
A tale as old as time, no matter if you were Team Pacey or Team Dawson. Each relationship was given its time to be explored and there was a natural conclusion that allowed each person to grow as a character.
Francis/Mary/Bash - Reign
As chaotic as it may have felt at times, Mary's relationships with both Bash and Francis were handled as well as a love triangle could explore them. A choice was made but above all else, the people involved had worth to the overall story beyond just the romantic element.