I have only once seen a UI animation that I didn't have to wait for. This was in the Metacity window manager, which had an option to animate windows minimizing/maximizing using a wireframe of their outline that could not be interacted with. The actual window moved immediately, and the wireframe did not obscure much of the screen while it moved. I would still turn them off, but if every UI animation was designed like this I would dislike them less.

That is a great design. Shows you where the minimized window is (in case your brain missed it) without making you wait. I would love to see an entire UI designed around the principle of "don't make me wait. Ever."

I think the best rule of thumb for UI animations is to keep speeding them up until users stop praising the beautiful/elegant animations. They shouldn't notice the animations.

I think iOS does an extremely good job at animations. They help convey movement/what changed/where did I just go, but they are usually so fast and subtle you don't realize there was an animation unless you try hard to spot them.