My Neon a/c has recently started draining my battery whether it's been used or not. I traced the battery drain down to the AC when I heard the compressor trying to kick in. The clutch on the compressor actually tries to engage each time I insert the fuse for the ac. If I leave the fuse for the ac in, battery will drain overnight whether the AC is ever used.

Look for a stuck closed ac clutch relay, or a short in the clutch coil windings

kitch428 is right about the A/C clutch relay being stuck closed. But, I don't see how shorted coil windings could be an issue.