Helping people with computers... one answer at a time.
An external drive is just another drive to Windows. Setting up programs on a drive that can be removed, however, warrants some care.
Windows XP-Home is installed on my C drive. Will programs, games and so on run if installed on my external E: drive or do they have to be on the same drive as Windows?
The short answer is yes, but there are, as always a few caveats and clarifications I need to make.
If when you set it up a program allows you to choose a destination drive to install onto, it shouldn't matter if that drive is C:, your Windows drive, or some other hard drive internal or external. For the most part they're all just drives, and the fact that the setup program gives you the option means there shouldn't be an issue.
For the record, if the setup program doesn't give you a choice then it may be an issue and I'd avoid trying to circumvent it.
Now, many external drives are removable. USB drives, for example, can be removed from your computer either while it's not running, or after clicking a "safely remove hardware" for the device. In the later case, if a program on your removable drive is running, "safely remove" may fail. All files on the external drive must not be in use, and a program running from the drive is definitely "in use". You'll need to make sure that all programs installed on the external drive are shut down before attempting to remove the drive.
Now, that sounds simple enough but more complex packages often install software that runs automatically when you start your machine, either in the form of explicit start-up menu items, or as system services. You may not think you're running any software that's installed on that external drive, but in reality it may have installed something that is. You'll need to figure out what that is, and take steps to disable it, or shut it down before you remove the drive.
Along those same lines, if the drive is not installed when you boot your system, you may get error messages on start up if a prior installation of software onto that drive also added startup items. Without the drive installed, those startup items may not be found, and errors may result. Menu items and shortcuts relating to the software installed on the external drive may also revert to Windows defaults until some time after the drive is reinstalled.
So there are a number of issues related to removable media, but if you're just installing your software to a second hard drive, and it just happens to be an external drive, I wouldn't expect that scenario to be an issue for you.