Yes. Start here:
Android SDK | Android Developers
Download the installer for your computer. Then you have to set up
emulators for the android device you have, and any others you fancy trying.
This can involve guessing the capabilities of the device in question, but it's not a huge problem.
At this point you can fire up your "device" on the PC, connect to the Android market (with your existing account details) and download whatever Apps you need. They will run just the way they do on the phone -- but a lot slower.
There was one "gotcha" in setting up the emulator, which i forget 'cos it was a while ago, but otherwise pretty painless. Oh, you'll be confined to a phone-sized display area, don't think you will be able to use full-screen on the PC...
'b