Shut down
A while back, while on a tech support call with Apple, I got into a discussion about sleep vs. shutdown for my desktop each night. The tech didn't think it was a real big deal either way, but suggested shutting down. I have done so ever since.
I experienced the "hanging shutdown" problem after Leopard install too. Instead of verifying the shutdown, I found that if I just left the dialog box open and let it countdown it eventually did shut down. If I did verify the shutdown by clicking the blue button in the shutdown dialog box, the computer would hang and I would have the spinning gear icon forever.
A few times it seemed that if I ejected and turned off the external (Time Machine) hard drive, I could verify the shut down by clicking the blue button in the shutdown dialog box and it would work. As it turned out, that was only intermittent and the problem persisted most of the time.
Now here's the strange part: the other day I opened up my Mac Pro to add another 4GB RAM (for a total of 8GB). After I installed the RAM, the computer now shuts down normally, as it always had before Leopard.
There was another little glitch after Leopard install: Before Leopard, regardless of what app (or apps) I had open, I could always click on the desktop to get the Finder menu bar at the top of the screen. After Leopard install, this didn't work anymore. After adding RAM, it works again.
I also installed Leopard on my 12" G4 PowerBook, and didn't have either of these issues.
Computers...