anyone got a good comparison program?

So, I was curious. Anyone know of a program which can compare computer files to see if they are identical? I'm looking for ones that do the following comparisons:

-- will locate files with identical date/time/name but different locations
-- will find files which have identical date/time but different names
-- can compare two files to see if their contents are identical, even if the names or date/time are different.

I'm betting that the first is fairly easy, the last hardest. Suggestions, preferably for things which are cheap or free?