If the only two choices are positive/negative (or thumbs up/thumbs down or some other equivalent 0/1 scheme), here's a formula that should work fairly well:

(n_positive + 1) / (n_positive + n_negative + 2)

So a single positive review gives you a score of .6667, and a single negative review gives you .3333. For large numbers of reviews, the score quickly converges to the actual fraction. If you don't have any reviews, you are at .5000.

The mathematical justification for this formula is that if you try to use a Bayesian approach to estimating the true probability of getting a positive review, and you start with a flat prior, this formula gives you the average of the posterior probability after observing the given number of positive and negative reviews. The full posterior distribution is a beta distribution with parameters alpha=n_positive+1 and beta=n_negative+1.

This formula is often used when applying Monte Carlo techniques to the game of go. I believe a lot of programmers simply start the counters of wins and losses at 1 to avoid corner cases (like division by 0), and they accidentally use the correct formula.