Quick way to tell if an installed application is 64-bit or 32-bit
Solution 1:
If you run the application, in Task Manager it should have a *32 beside it to indicate it's 32-bit. I'm pretty sure they had this implemented in Server 2003, not positive though, hopefully someone can clarify.
You could also run it through PEiD. PEiD does not support 64-bit PEs, so it will choke if it's 64-bit.
There is also the famous GNU file for Windows. It will tell you all sorts of information about an executable.
Example:
$ file winrar-x64-392b1.exe
winrar-x64-392b1.exe: PE32+ executable for MS Windows (GUI)
$ file display.exe
display.exe: PE32 executable for MS Windows (GUI) Intel 80386 32-bit</pre>
As you can see, the 64-bit WinRAR installer is classified as PE32+, which signifies a 64-bit executable. The 32-bit application is simply PE32, a 32-bit executable.
Solution 2:
The easiest way, without installing another program or running the file, is just to right click on the file, choose Properties, and then go the the Compatibility tab. If there are no greyed out options and Windows XP and 9x modes are offered, it's 32-bit. If there are greyed out options and Vista is the earliest mode offered, it's 64-bit. No need to start the application at all.
If the application is already started, you can of course still use the *32 idea mentioned in other answers. However, this is not available in Windows 8.x and its new task manager. Fortunately, you can enable a Platform column by right-clicking on the column headers in the Details tab and choosing Select columns. The column will contain either "32-bit" or "64-bit" as appropriate.