In the company I work for no shutting down anything in a twin, and you may shut down 2 (2 & 3) in a quad if you're somewhere like JFK with a very very long taxi time to the runway.
On the way in it's OK to shut down two (2 & 3) if time is suitable and the cooldown times have been met.
Benefit: Saving FUEL and you may still make your destination without a tech stop. (A normal taxi out can cost up to 1.5 tonnes in a 747 and alot more for abnormal).
Disadvantage: when you're heavy you'll look a little silly having to put on a heap of thrust to get moving each time you stop.
If you're unexpectedly cleared for take off when the other aircraft ahead go back to the gate for more gas and you don't have them all turning and burning you may look silly as well
(they may require a 5min warm up so start em, warm em, and then shut them down).
I saw a post saying that some US? carriers shut down a donk on the 737s but don't quote me.
Some places charge for ground power etc. so may as well use it, problem is sometimes it's unreliable and also ground aircon can do a poor job in hot/humid weather. Beancounters usually decide where and when APU's should be shut down, but a little common sence is a good start.