Funnily enough, love triangles come immediately to mind. I like to think any trope could be pulled off successfully, but the back-and-forth game of "which one are they going to choose?" is frustrating to me as the reader in 99% of cases and has soured several once-favorite stories of mine. Especially when the center of the triangle doesn't end up with the character I was rooting for- or worse, I didn't like either love interest to begin with (ex: disliked all three love interests Chaol, Dorian, and Rowan from Throne of Glass- and, actually, Celaena herself too :p).
I can't think of any love triangles off the top of my head that I didn't loathe with burning passion... However, I preface all this with "funnily enough" because I actually have something in my story that sorta unintentionally resembles one ahaha
It doesn't include any sense of competition or rivalry, and no one "likes" more than one person at a time. It's actually more of an unrequited love trope, and the 'triangle' is more of a 'line'.. with one relationship ending before the next begins. Nonetheless, ever since I realized "aw crap, this looks like a damn love triangle" I've been thinking hard about how to handle it thoughtfully and avoid all the things I hate about these.
Though it makes a lot of sense within my story's setting, I'm definitely guilty of the missing parent trope though. Actually kept my protagonists' parents alive at the beginning of the story to avoid falling into this completely, but it's established early on that they don't have much time left due to a deteriorating illness.