There are actually two programs for comparing files on a word per word basis. wdiff is a front-end to diff as found in the GNU diffutils package. It is quite mature. Its planned successor, wdiff2, is a front end to mdiff, and as experimental as mdiff itself. See Experimental.
A word is anything between whitespace. This is useful for comparing two texts in which a few words have been changed and for which paragraphs have been refilled.