When I need this I just look at the nearest object. If the first letter is between a and m, that's a 0. If it's between n and z, that's a 1. For larger strings of random bits, take a piece of memorized text (like a song you like) and do this with the first letter of each word.
[Aside] When do you need to generate random numbers in your head? I can think of literally no time when I've needed to.
Another monthly installment of the rationality quotes thread. The usual rules apply: