Can I run minecraft on windows 98 or windows 2000?

Theoretically, yes, because all it requires is an updated version of Java. I don't think that Java still supports Windows 98 however. I can't say 100% from experience because I haven't tried it, but I can say with a good amount of confidence that it probably is not going to work. Honestly, give it a shot, it's at least worth a try, but I'm going to assume that Java doesn't support Windows 98 anymore.

I don't think so, Minecraft need java 6 and up to proper running and java itself need windows xp and up. I would guess that their is a chance that it would work on windows 2000 as it is pretty close in architecture to windows xp. I would not have much hope for Windows 98.

Edit: According to:

http://www.oracle.com/...35212.html

Windows 2000 is supported by Java 6 so you may be able to install this version instead of Java 7 with Windows 2000 and play successfully. Hard to say for sure before actually trying it however.