There are several ways to find out; here are a few simple ones.

For Windows 7 or Vista

1. Click on the Start icon.
2. Right-click on Computer and select Properties.

For a 64-bit version operating system, 64-bit Operating System appears for the System type under System (as in the screenshot below) whereas for a 32-bit version operating system, 32-bit Operating System will be displayed.

– Or – 

Click on the Start icon, type system in the Start Search box, and then click system in the Programs list.

– Or – 

In Windows Explorer, go to Control Panel\\All Control Panel Items\\System.

For Windows XP

Try one of these two methods:

First method

1. Click Start, and then click Run.

2. Type winmsd.exe, and then click OK.

Alternatively you can type msinfo32 (instead of winmsd.exe), note this also works in the Start Search box for Windows 7 or Vista.

3. When System Summary is selected in the navigation pane, locate System type under Item in the details pane. Note the value.

• If the value that corresponds to System Type starts with x86, as in the screenshot below, the computer is running a 32-bit version of Windows.
• If the value that corresponds to Processor starts with IA-64 or AMD64, the computer is running a 64-bit version of Windows.

– Or – 

Second method

1. Click Start, and then click Run.
2. Type sysdm.cpl, and then click OK.
3. Click the General tab. The operating system is displayed as follows:

• For a 64-bit version operating system,  Windows XP Professional x64 Edition Version < Year> appears under System.
• For a 32-bit version operating system,  Windows XP Professional Version appears under System.

For additional information, refer to Microsoft Support website: http://support.microsoft.com/kb/827218 and also http://windows.microsoft.com/en-US/windows7/find-out-32-or-64-bit or FAQ: http://windows.microsoft.com/en-US/windows7/32-bit-and-64-bit-Windows-frequently-asked-questions or check http://whatsmyos.com/.