Sidequests make good games great. Most solid games are playable to just about anyone, but to really pull a player in, to give them a chance to finish up and walk away and have them choose to play on and get more is the sign of a great game. It's already been written plenty elsewhere but the power of games lies in the close relationship between the audience and the work. If the audience can end a story but decides not to because of their intimacy with it than it speaks to the strength of the work. But sidequests can be fickle creatures and they seem more prone to making cumbersome distractions rather than added depth.
Even in the sandbox, which is a game composed nearly entirely of optional content to be discovered, so much is artificial padding repeated over and over again for the sake of completionists. A sidequest ought to do more than pad the length of a game. It ought to be so compelling by itself that skipping it would eliminate the sense of closure that comes from finishing a game.
That isn't the same as making it a part of the main plot. The "side" part of the quest means that the plot can be completed without it, but being offered a chance to stay in a game's world, with its vibrant characters and master its mechanics should be an opportunity, not a chore. Many sidequests end up like the single-player gimmicks tacked onto the Soul Calibur games where opponents cheat more audaciously or the time-sinks found in the Grand Theft Auto series. Even Legend of Zelda's normally amusing diversion are so ludicrous that they make no sense in the game's context (does Link really need to spend twenty hours hunting bugs for a bigger wallet when the world is ending.
Contrast these with Batman: Arkham Asylum's Riddler challenges. They're a fetch quest at best and at worst they literally require you to take time away from the game to stare at walls. But Arkham Asylum's quests weren't criticised, they were justly praised. Because they drew attention to the level of detail that was put into the world, they tested the player's skill and ingenuity and they provided background exposition to the events in the story. Mechanically, they could easily be avoided, but not taking up Mr. Nigma's challenge was giving up on a huge appeal of the game.
For me, no game has managed sidequests better than Chrono Trigger. At the end of the game, just before the player is ready to take on the big bad, the team's mentor lists a series of wrongs throughout the game that can be righted. The heroes can waste no time and get back to the business of world-saving, but the sidequests provide so much more worthwhile content. Not only are they greater challenges and provide huge in-game rewards but they also resolve many of the conflicts for the individual characters. Everyone the player has gotten to know and care about in the game gets their brief period in the spotlight.
Sidequests aren't necessary for a good game. That's the point. But how much more did the tapes in Bioshock immerse you than the generic laptop scans in the first Modern Warfare. When they're done, they're worth doing right and their purpose is not just to waste more time with a certain disc in the tray.