I have a Maxtor 100GB external HD.

For some reason, when I plug it into the USB drive of my computer it starts beeping. Not the computer, but the actual hard drive. Then it doesn't appear in my computer, however the light on it comes on.

When I remove it my computer makes the sound that it does when it is normally removed.

Any ideas what the hell is going on?

It's cooked like a thanksgiving turkey.
That noise is most likely an alarm that the HD is using to announce internal distress.
I hope there wasn't anything important on it.
I'm putting my GAS on hold
for a couple months in order to pimp my ride.

Don't judge me.
Never fully trust any HD
Backup your backup units when you can. I keep DVDs even though I have a 500GB external Phantom Drives backup unit.

It does sound like your drive is failing though and there's some alarm going off, try to find something about that in the manual.
Perhaps it isn't compatible with your pc - e.g I tried installing memory which wasn't compatible and it beeped uncontrollably.