The truth is that I love the side quests in this game. They are incredibly well thought out and implemented. Like others in this thread, I really enjoy the Random Events. The races are a lot of fun (and not just Franklin's, but the ones out in the desert, the off road ones). I actually really like doing the collectibles, too, when I play through a 100% campaign because the scenery is so enjoyable.
Nobody mentioned the Base Jumping yet, and those are some really fun ones, with some gorgeous scenery. I enjoy the hell out of Trevor's gun running missions, and totally agree with SabreGT that they are very reminiscent of both the two original Smuggler's Run games, which I really loved for their time.
I also like some of the newer side missions, like races and such, in the Returning Player Bonus and next gen console versions.
I think the Sea Shark races are fun as hell, very reminiscent of Saints Row 2's jet ski races.
I also LOVE the Bail Bond missions, more for the wacky dialog and story, even if the missions are a tad blah in terms of action. Still on a new save I always look forward to them.
Surprised nobody mentioned the Rampages! Hahahahah those are just stupid fun!! I may be in the minority in the forum, but I actually really enjoy both the Stunt Plane Time Trials as well as the Flight School. They are easy and a really nice way to enjoy the scenery with checkpoints and such.
One thing that I am actually very surprised that I enjoy as much as I do is the hunting. It is actually really enjoyable, once I get myself into a mindset to avoid hostile animals attacking.
Although, I am absolutely NOT a fan of the yoga, Golf, or Tennis, and I find them mind-numbingly tedious, I think the game is better for having them in there as an option to play as side missions. I will say, on a side note (lol no pun intended) that after a bunch of playthroughs of this game, I have to grudgingly agree with the people who complain that the storyline forces you to play a full out Yoga session to advance. Again, I think the game is better having these activities I don't like, because GTA should be all about choice and letting people find their own fun. But if they really wanted players to be forced into Yoga, they could have added a very abbreviated version to that mission. The Tour Bus is another one I find incredibly boring, BUT have to admit it adds to the game and the game is better for having the option to do it.