I've been using 123D Design from Autodesk for a couple of weeks without issues, but yesterday, the program froze and when I restarted it, I received a Windows message:

123D Design has stopped working

A problem caused the program to stop working properly

Windows will close the program and notify you if a solution is available.

I uninstalled and reinstalled the program but at no avail. I keep receiving the same message, even after restarting the PC.

I'm using Windows 8 64bit.

I would suggest you to delete the program traces related to 123D design completely from the computer. Re-download the 123D design software try installing it.
The downloaded file might have gone corrupted so asked you to re-download and re-install.
No worries, let's try place the computer in a clean boot state and check if the issue appears.
You can start Windows by using a minimal set of drivers and startup programs. This kind of startup is known as a "clean boot." A clean boot helps eliminate software conflicts.
How to perform a clean boot to troubleshoot a problem in Windows Vista, Windows 7, or Windows 8
http://support.microsoft.com/kb/929135

Note: Follow Step 3 to reset the computer to start as usual after troubleshooting with clean boot.