Basic 741 Op Amp Question
I agree with Oli:


  If you have another chip, try that to make sure this one is not blown.


If they both do the same thing, then this smells like a case of phase-reversal. Op-amps have a valid common-mode input range. In the case of an LM741 (datasheet from www.national.com), the +/- 15V supply range yields a guaranteed +/- 12V common-mode input range. Outside that range, it used to be common for the output gain to sometimes reverse sign, causing positive feedback rather than negative feedback and the output to saturate at the rail until it came back into its valid input range.

Modern op-amps are carefully designed to not have this problem, because it's confusing and nasty to debug. Which is one of several reasons why my tongue-in-cheek comment ("basic 741 opamp answer: there's always a better op-amp to use") is good advice. There are plenty of cheap and good op-amps that have much better performance specs than the 741. 

This webpage seems to indicate the 741 doesn't suffer from phase-reversal -- the ones that do are JFETS -- so maybe it is just your chip that's busted --  but I'd use the LM358 instead.