The new Mac App Store can be a useful way to find software for OS X, but a few people have expressed their dislike of the store and prefer to not have it on their systems. Some have even avoided updating to OS X 10.6.6 to prevent the store from being put on their systems. While this is one way to avoid the store, doing so will also prevent you from benefiting from the latest security and bug fixes that future OS updates will bring.
The requirement of OS X 10.6.6 for the Mac App Store allowed integration of the store into the Apple menu, but if you remove the store then the system will revert back to the old setup, in which the Apple Menu shows "Get Mac OS X Software" and will link to the Apple software downloads page instead of opening the store application. Granted, this is not a supported option by Apple, but it's an option that for now seems to work.
Some people have been concerned about the "storeagent" process that appears in the OS X Activity Monitor window in OS X 10.6.6. This process located in the "Commerce Kit" framework that is part of OS X 10.6.6, and is set up to run on demand when the store is open, and appears to be a version manager to help the store notify you when updates are available, or to inform the store that a software package is already installed.
As with the Mac version of FaceTime, the direction and effort Apple is taking with the new Mac App Store are a bit unclear. Apple could leave it as it is, as a third-party software discovery and maintenance tool, or could integrate it further into the OS and merge it with the Software Update feature to manage both system and third-party updates. Only time will tell, but for now people who wish to not have the program on their systems can easily remove it by deleting the program.
Update: MacFixIt reader "Bill" wrote in suggesting that if you need to add the App Store back, you can always reinstall it by running the Combo updater for 10.6.6, or for later versions of OS X when they become available. In addition, if you have a Time Machine backup or other backup of the application, you should be able to copy it back to the Applications folder and then run a permissions fix on the boot drive to get it running as it was initially installed.