Least favorite, in general, is insta-love. There's attraction, okay, but insta-love is BS. lol. You just don't see someone on the street and go "omg I love you, and will never hurt you and will worship you for the rest of my life, no questions asked". I know it's sort of a thing, with shifter-series', and I can sort of understand that with them not being entirely human; but even then, the better writers will have conflict there, where it's not insta-love, but a war between their shifter and human parts.
Another would likely be mystery-guy-is-the-one type relationships. Especially those stories told from females' perspective. Just.. so predictable. Ever since seeing that [bleep] in Twilight, every author seems to do that now with highschool age drama stories.
The "arch-nemesis" that isn't much more than a loudmouth or generally a brat, or a mean-girls type trope, is another one I tire of. lol
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As for favorites..
I like stories that are well plotted, where you'd have to read the entire series more than once just to catch all the little breadcrumbs and hints that are in the next bit of the story. A good example, IMO, if you're a reader, is Throne of Glass. (Warning though, the later books (i think 5th or 6th) in the series have more adult scenes). It's fun to read back and see what you missed that the author teased but you didn't catch the first time. It also makes you double-think what may happen in the next book, or what that one thing meant back in book 2, or whatever.
For relationships, I prefer the more head-butting or strangers learning eachothers' personalities, weaknesses, and learn to be friends, then more; but not a change of heart over one incident or within the same chapter of writing. lol [what can I say, I'm picky, and I read a lot]