3 Answers

There are a couple factors to consider when deciding to pick eggplant:
Size – Pick eggplant when they get to be a little bigger than your hand. As with other vegetables, it is better to pick eggplant when they are young and tender. Picking them early will also encourage the plant to grow more, and will help to extend the growing season. The eggplant does not have to be those behemoths you see at the supermarket.
Shine – An eggplant is ready for the picking when it gets a nice reflective sheen to it. Grasp an eggplant you might think is ready, and carefully hold it up to the light – if it appears to be very shiny, it is ready.

When they're purple, firm and sound hollow when you tap it. It should release easy from the vine. 

...at 3 past 10 in the morning!  ha, ha,   Just kidding, when they are purple (unless they are a variety that is other than purple) and firm but not too big.  I like to actually cut them, as it prevents the plant from damage of being torn off, which rips at the stem of the plant.