When is it appropriate to mount components at a 45 degree angle?

Another reason would be for indicator or display components. It's not terribly uncommon to see chip LEDs at varying angle to fit the aesthetics of a particular device.

Whatever the reasoning, most SMT machines can places parts at angles without issue.

Placing a QFP chip at 45 degrees can make it easier to connect the leads to pins on a DIL board. Try it for yourself. Other angles aren't helpful.

Parts can be at whatever angle they need to be to help layout or fit into some bizarre package. Your manufacturing engineer may not like it, but if it's required, then oh well. As Duane mentions, this is rarely a problem nowadays, but be sure.

Conversely, your manufacturing engineer will pretty much demand 45° rotation of QFPs if they are to be wave soldered.