Being inconspicuous takes practice, skill and cunning. Here are some things that I've learned about staying anonymous.
Step 1: Dress for success
Dress so you don't stand out. Normally this means dressing plainly. Although, sometimes you may need to dress up like a zombie to blend in with a crowd.
Anticipate what the rest of the crowd will look like and use common sense. Avoid bright colors or revealing clothing. Avoid anything that could get people to pay attention to you. Avoid being too out of style and too in style. Avoid things with big logos or graphics on it.
In most situations the ideal outfit has dark muted colors, is clean, covers your naughty bits and matches. It should have a timeless look.