A number of people who have installed OS X 10.6.6 and have been using the new Mac App Store are finding that when downloading applications the App Store seems to hang, sometimes showing the spinning color wheel and other times just pausing with no indication of progress.
Some people who have experienced this problem have found the issue seems to be caused by the presence of certain hard-drive volumes. These include some external drives, but in particular the problem seems to be caused by the presence of Boot Camp partitions. Unmounting and disconnecting the drives seems to get the application working again.
This could indicate an incompatibility with Boot Camp and require an update, but it could also be an issue involving the new OS and applications during an initial "break-in" stage as various caches and configurations are checked and set up in the system. If you are experiencing this problem, there are some things you can try that may help clear it:
Boot into Safe Mode
Boot into Safe Mode on the system by restarting the system while holding the Shift key. This will cause the OS to clear some caches and temporary files, which will be rebuilt when the system is restarted normally.
Perform a permissions fix
When in Safe Mode, open Disk Utility and run a permissions fix on the boot drive. Do this in the current OS X installation and not off an OS-installation DVD, because the latest update will include additions and changes to the permissions library.
Do not use third-party utilities (yet)
Lastly, while it may be tempting to try a full cache-cleaning routine with third-party utilities, for now it may be best to avoid using them until it's been confirmed that they work properly in the latest version of OS X. Check with the developers to see if there are any updates or compatibility issues before using these utilities.
One thing to keep in mind is the App Store is an online service, and many people will be trying to access it all at once. Apple's servers may periodically experience slowdowns, so another approach might be to just give it time and allow queued downloads to eventually start. If there are server-related malfunctions Apple will have to address them, and this can cause pauses and delays.