I like them when they give me excuses to explore, but I hate Random Drop, 20 Bear Asses type sidequests.
Eating a Vanilluxe will give you frostbite.I don't really mind 20 Bear Asses-type sidequests.
I wish there were more sidequests like FF XII's hunts. I found them both challenging and fairly rewarding. =d
Two games that did sidequests right: Majoras Mask and The Wind Waker.
I'd say that a good sidequest has to have at least a few pieces of unique dialogue, and a cool reward at the end.
I absolutely adore sidequests which is one of the main reasons why I am so obsessed with Suikoden.
They just give me a feeling of freedom because of their optional nature.
I love sidequests. They add a ton of replayability to games without being cheap about it. I feel like I can get a lot more out of a game when I can go back after I beat it and spend a ton of time doing sidequests and whatnot.
I used to enjoy them, but for whatever reason I've completely lost patience for them and prefer to ignore them now. I especially hate sidequests that require you to follow them throughout the entire game. The tolerable sidequests are the ones that patiently wait for you to be at endgame, but by that point I'm usually eager to just finish the game.