In my company, we have several ex-employees. On my Windows Server 2003 machine, there is a "profile" folder which contains the following folders for different employees: "Application Data", "Contacts", "UserData", "WINDOWS" and so on (e.g. profile\employee_A\UserData). If I copy the folders to a local machine and back them up, do I need leave the data in the "Profile" folder? Or to put it differently, will removing the files and folders from a previous employee's "profile" folder cause any problems with Active Directory or some other software? Thanks, in advance, for your help!
AD won't have a problem with this in the slightest. It stores all its information on users in a database on the domain controllers, along with its information on everything else.
As for the "some other software", that rather depends on the "some other software" and whether or not you're likely to use these accounts again (I'm assuming that if you were 100% positive that these were dead accounts that would never be touched again you'd just be deleting them...).
You're unlikely to break other "server level" software by doing this but clearly if someone's desktop software (for example, office) is storing a lot of custom settings in their profile and you delete the profile then the desktop software clearly won't be able to find its settings if anyone logs into that account again. Only you can say for sure if that's a problem or not... it shouldn't be a problem for most things but none of us here know if you're running "Crazy Joe's accountancy software" under the ex employee's ID (crazy joe is known for being the home of both crazy things like storing important data in profiles and for being the patsy whenever i need a company name for my contrived examples).