Yes, you can.
I've fried quite a few things by accidentally crossing the leads.
As far as killing something that isn't on, you shouldn't be able to, but it's still possible as capacitors will retain a charge.
You could also kill extremely sensitive components with the DMM's "test" voltage, for measuring resistance for example, but this is usually very low.
Originally posted by: CallMeJoe
Originally posted by: slpaulson
The surge protector wasn't on?
I suppose you could have discharged a capacitance.
Otherwise if you were measuring current, that's pretty much a short. That path has a fuse, but you could certainly still damage something.
Some multimeters have an unfused high-current ammeter connection; IIRC, my old Fluke 77 is fused on the 200mA circuit, unfused on the 20A circuit.
Both circuits will be fused.