Depending on your definition of ruining a wall, the best way I know is screw through into studs, or use wall anchors depending on how heavy.
See here in this DIY video what they do:
7:29 using metal carpet transitions.
If its a rental... be smart and buy some Spackle. Most landlords I've had are cool if you Spackle the holes. I've only been asked to repaint once, which had nothing to do with Spackle.
For bass traps... if you're just using the the foam corner peices... good double sided tape or tacking nails should work. You could try poster putty or whatever they call that stuff... or even some of that 3M Control Center adhesives for posters and lighter weight stuff.
Just some ideas.