I have had great success with the "Rat Zapper" which is designed for
small rodents such as rats, mice and chipmunks. I installed a partial
cover (duct tape) over the opening so that mice and chipmunks can
get in, but squirrels can't. The trap is not lethal for larger critters such
as squirrels - they just get a jolt rather than a fatal dose of electricity.
The unit costs about $30 and is very good:

http://www.agrizap.com

I've had some luck with snap traps (mouse traps). The biggest problem
with them is that squirrels will get into them also - they set off the traps
and are strong enough to free their leg from the trap. Also, birds get killed
in the mouse snap traps.

Pellet guns work well. Don't waste time using BBs if the airgun will
accept pellets. And use field points rather than the less effective blunt-
nosed pellets. A modestly priced pellet gun ($25-$45) plus an inexpensive
scope ($10-$15) will make head shots on rodents rather easy from a
considerable distance. Body shots are ok, especially on chipmunks,
if you don't mind the risk of a somewhat slow kill allowing the injured
rodent to run over to your neighbor's house and possibly dying in front
of his wife or kids. That's particularly important if you're in the city and
your are breaking the law using the pellet gun. Not that any of us would
do that.

Gideon