Long, long time ago there have been a rumor that there is a virus able to infect gifs. All the wise people laughed at the idea of data executing code. But then, buffer overrun attacks have been discovered, and a bug in Internet Explorer that allowed buffer overrun in gifs, essentially executing malicious code.
The moral of this story is a double-ended one. First: there is always a possibility that data could be used as "viruslike" attack vector. Second: There was absolutely no possibility any virus-scanner could have detected it before attack was discovered.
I can only recommend scanning data files if there is a known attack which could compromise users during regular usage (and your AV detects it). Scaning every .txt for being renamed .exe seems bit overkill. More importantly, you should be ready to re-scan old, EXISTING files, in case a new attack is discovered. Scanning existing files is easy, the problem is what to do next - witholding access to the file, notifying it's owner, etc - it's a lot of work to design and implement such error-handling.
As raz said, pdfs are different beasts: they are already known to contain code and have to be scanned both on upload, and in storage in regular intervals.