Goof-Off is very caustic, and will readily damage many plastics and paint. However, it is an object lesson in
salvation. (Ever think sometimes the Internet is
too big?)
Goo Gone is a completely different product, and I've never had any problems with it. Great for removing price stickers, etc., from just about any surface. It's the first thing I reach for before taking more drastic measures.
I've never tried it with gum, but I'm confident that at least it wouldn't cause any damage in your engine compartment.
Here's a handy "idiot proof" shopping list:
