Originally Posted by pineman19
On the average, I would say 18-24". I wouldn't go much less or too much more in mountain streams. Too close, and the dropper won't have enough room to do its thing, too much and you'll have more problems with tangling etc. TRy a few different lengths and see what works best for you. Most times, it's best to use one size smaller tippet for the dropper to help with casting and movement of the second fly.
Good advice here from Neal,
Might I add a few more pointers that work for me. Often when using a dropper, I actually prefer fluorocarbon tippet for the dropper. Using fluorocarbon tippet serves two purposes, it is more dense than mono so it actually sinks easier and gets your fly down quicker plus it is harder for the fish to see. A perfection loop on your dropper can also be handy to add some more action to the fly as well... but that's just what I do.