After Effects has been tested with Windows 7 and there are currently no known issues. Windows 7 looks to be a great OS to run After Effects.
I highly recommend the 64-bit editions for 2 main reasons. First, After Effects CS4 runs better on 64-bit operating systems, and second, After Effects CS4 will be the last 32-bit version of After Effects. I also highly recommend the Professional or Ultimate edition because the Home edition is limited to 8GB of ram.
Adobe has posted an FAQ discussing Creative Suite support for Microsoft Windows 7. For more detailed technical info, see the technote on “Installing and using Windows 7 with Adobe applications.”