It depends on what you define as "a bunch of files". If you are referring to documents, music, photos, etc...yes, you can copy them to any computer you wish and open/modify/etc them.
What you cannot do is copy programs from one computer to another. I've seen people try to just copy their Program Files from their old computer to a new computer, and then they wonder why they don't work. There is more to your programs than just those program files you see (lots of registry stuff, too).
So if all you want to do is copy your data (documents, music, etc.), then, yes, you can do that. But if you want your programs on the new machine, you will have to install them like normal. And if your old XP programs are fussy when installing, try Compatibility Mode
Does that answer your question?