Install the v10.6.6 Combo Update here.
If after you install the combo update, you will have problems with the app, follow the instructions here.
See: "If the Mac App Store application was removed after installing the Mac OS X v10.6.6 Combo Software Update"
I'm having a similiar issue. Every time I start the App Store, the user interface appears for about 3 seconds, and then it crashes with an error message "The app store quite unexpectedly".
Process: App Store 
Path: /Applications/App Store.app/Contents/MacOS/App Store
Version: 1.0 (54)
Build Info: Firenze-540000~6
Code Type: X86-64 (Native)
Parent Process: launchd 
Date/Time: 2011-01-07 20:19:08.082 -0600
OS Version: Mac OS X 10.6.6 (10J567)
Report Version: 6
Interval Since Last Report: 3915 sec
Crashes Since Last Report: 13
Per-App Interval Since Last Report: 44 sec
Per-App Crashes Since Last Report: 13
Anonymous UUID: 4BB462AA-3C21-4CF0-9F77-930B0982ACC2
Exception Type: EXCBADACCESS (SIGSEGV)
Exception Codes: 0x000000000000000d, 0x0000000000000000
Crashed Thread: 0 Dispatch queue: com.apple.main-thread
I applied the combo update also, but that doesn't help. I run it in safe mode, but that does not help either. Any suggestions?
I got exactly the same problem when firing up App Store or Safari. Installing the combo update didn't work. I managed to solve the issue by removing Safari and reinstalling it again. Here's a link for safari http://www.apple.com/se/safari/download/
I'm having a similar problem.
When I try to open the App Store app, the icon bounces up & down the dock for a few seconds before disappearing without any error message. Needless to say, the App Store doesn't launch.
I haven't tried to download & install the update linked above because I already have OSX 10.6.6 installed and 'Software Update' tells me that all my software is up to date.
I should mention that I restored my machine from a Time Capsule back-up today after some things went awry with BootCamp, but as far as I can tell everything is back to normal since the restore; except for the App Store app.
I had exactly the same issues as everyone here after a fresh install of Snow Leopard on a fresh Hard Drive. After the clean install, I went straight for the 10.6.6 combo update. The App Store either stuck on the 'Loading' page, or would just bomb out with the 'Quit Unexpectedly' error. I fixed it last night:
LONG story short:
I called Apple Support today and although my MacBook is out of warranty by a year, they tried to help. 3 hours on the phone I was at the same point I was before I called. It's now escalated to 'Engineering'.
1. Install from the Snow Leopard DVD over the top of the exisiting install which preserves all users, data & Apps. This returns your 10.6.6 OS X back to 10.6.0
2. Download each 10.6.X update manually - I didn't download 'combo' updates other than 10.6.5 as that's all I could find, but it didn't matter as it turned out.
3. Install each update in order, reboot and then install the next.
4. After 10.6.6 update (not the combo update) it worked again.
I had previously installed 10.6 on a fresh hard drive as a test and had upgraded straight to 10.6.5 combo and then to 10.6.6, but the App Store was broken still.
My best guess is that there is something in one of the previous updates to 10.6.5 which the Mac App Store depends upon.
I have the same problem but it is worse.
After some kind of crash during the night (I was not able to access the computer in the morning) , I have the following symptons:
1 - App Store does not work;
2 - Software update does not work;
3 - I am now able to install any kind of software, including as suggested 10.6.6 combo;
4 - Safari won't start, it freezes as soon as the first window shows up (and it does not render any images);
Do I have to install SL all again?