I deleted App Store on my Macbook, and reinstalled it using the Combo Updater 10.6.6. Now, when I run it, it starts dancing in the dock briefly and then just disappears, and doesn't run any more. I experienced this with some other applications as well, for example Paint 2. Could someone explain what's going on?
10.6.6 didn't have the AppStore. It was added at 10.6.8, therefore I assumed you had this.
Okay, that won't work on Yosemite (10.10.x).
Therefore, delete it again via Terminal "sudo rm -rfv /Applications/App\ Store.app/"
Next step, rebooting the computer, holding CMR key and R pressed. You'll end up either in the local recovery or if not present, your computer will download the internet recovery. And now choose 'reinstall OS X' This will give you back any missing system files without deleting anything.