afremont:
What datasheet spec will tell me how close the output can get to 0V with a single supply? Another poster mentioned 1.25V, that seems a little high to me.
Like I already said, the output can go right down to 0V provided you don't ask it to sink any current. That's why the first page of the datasheet http://www.ti.com/lit/ds/symlink/lm124-n.pdf says "Large output voltage swing 0V to V+ ? 1.5V". If you do ask it to sink current, you'll find the maximum sink current quoted at 2V and 0.2V output voltage on page 4.