There are exceptions to every rule with this subject. Media blasting is ok for lots of parts, but it depends on what abrasive is used, and how talented the blaster is. It leaves a very nice finish on lots of different metals and alloys, and is a perfect substrate for painting or powdercoating. Obviously engines won't like blasting media getting into them, and IT WILL unless everything's SURGICALLY clean.
Chrome can be cleaned well with Mothers as mentioned already, and the aluminum can be polished with it as well. There are many methods to clean and/or polish the aluminum parts. Just do a search here, or on google and you'll find loads of options. Paint can be rubbed down gently with something like a very fine rubbing compound to brighten it up after years of oxidizing. Not always salvageable though.
If you see my wheel interchange thread, then you'll see the finish that is left on cast alloy mag wheels, after being blasted with glass bead. My frame was blasted with aluminum oxide, and turned out awesome after powdering.
That help any?