If I was confronted by me, both me and me would turn to someone else and say, "I think i've gone insane." And upon noticing that we both said that in unison we'd both go, "Duuuuude! I've been cloned!" And then say, "I wonder which is the original....eh... bad direction to go in." And then go about our day. Stupid homuculuses. So easily doubting the validity of their existence. Bah.
In my case, both would probably just stand there for a short while, observing each other, eventually exclaiming something along the lines of "Hmm, how... interesting. Quite unexpected.", and then proceed to briefly examine and attempt to verify the existence of each other in some way. After that, both would go "Err...? It appears I have been duplicated. When did that happen, why, ...and how?", and begin a discussion, in which we would attempt to find out any differences between us and in our experience.
Then, provided there would be no grounds for hostility, we would make sure to keep in touch, eventually joining forces; as there is a lot of stuff that I'd like to finish that I don't have enough time for, we could alternate between working on different things, accomplishing twice as much when possible, and halving the worldload when needed.