I take a different viewpoint. As I've said before, weight is simply a means to increasing the difficulty of the movement. If the movement needs a lot of weight to make it hard then isn't the movement itself a little too easy? A movement that requires less weight to be considered very difficult is actually a more efficient use of the weight available to you. Those of you blessed with piles of iron obviously don't see the value in this. In a way, you're kind of the strength training version of pampered house pets. Welcome to the jungle! Out here, we learn how to make the most of the least. Unilateral work is the way we can do that.
Ben Bruno wrote a pretty good article over at T-Nation where he described his year-long experiment with training his lower body, one leg at a time. Apparently, he did this in response to a back injury. The single-legged approach was more kind to his back. I've heard this approach parroted by a couple of sports-based strength trainers. I can't comment on it since I don't have an injured back and I haven't done a lot of the work he described but he obviously learned how to get some serious leg training within his limitations. Iron junkies might balk at the notion but it still worked very well.
This guy seemingly never takes the weighted vest off... allegedly not even for sex.
When we move to single-limb, upstairs version, we come to one of my favorite ways to train the upper body, as well as another reason why unilateral work is so awesome: it's a great, great way to strength train under time constraints. Just simply blast one limb, doing a movement until you're exhausted. All you've got to do is break long enough to catch your breath (a little) and then do the other side. It's possible to get a lot of work in a very short period of time training like this.
Oh, and training on one arm can be brutally difficult!