I don't have any experience with vests myself, but it sounds like they would be great in moderation, and a much easier way to make bodyweight motions harder. Holding a dumbbell between your knees for pull ups can be a real pain.
However, don't use wrist or ankle weights for running or anything like that. They could destroy joints. It's all about the physics.
Basically, if you run with an ankle weight, every step forward the weight pulls on your knee a little, then it slams back together when you land. Boxing with wrist weights does the same thing to your shoulder.
What they are good for, are motions that would be really hard to add weight to otherwise, like side leg raises or leg raises:


Or if you're between weights on dumbbells and need a creative way to fill that gap. Say 20lbs is too easy, but the next you have is 25 and that's too much. A 2lb wrist weight could be useful to help you bridge that gap.