Transitions are very like makeup. If the user notices them, you may be doing something wrong. They should blend into the entire experience and be natural. Some of the examples in that article are good, like showing things coming from something you clicked on (another example of this is the OSX dock) or moving to a sub-page using a wipe effect.
VisualEditor is using a couple animations (powered by CSS3, woot!) to make visual connections between different states. I think it really has helped make the user interface feel smooth and fluid - but in experimenting with them I've also found it's possible to make an interface feel less responsive, and even really annoying.
Gotta know when the improvement ends and the flashy (read cheesy) effects start.
- Trevor