Chrono Trigger is a great example, obviously, as is Final Fantasy VI. Pretty much the whole second half of the game is side quests.

The Mass Effect games also have really good side quests.

I like older games where the side quests actually made you do unique stuff rather than just 'talk to this person', 'kill x of this monster', 'bring me this item'.

Probably my favorite side quest ever is the trading game in Link's Awakening.