Probabilistic algorithms often have a parameter that allows one to tune the error rate, typically by running the algorithm repeatedly. This often gives an error rate of something like $2^{-k}$ for $k$ iterations. This is a fine situation to be in, because $2^{-k}$ can be made as close to $1$ as you like without having to make $k$ very big at all. At this point, the theoretician sits back contentedly, his or her job done.
In practical terms, though, are there any guidelines as to which value of $k$ should one choose? Obviously, there's no universal answer, since the answer in any particular situation will be a trade-off depending on the importance of avoiding errors and the cost of doing more iterations.
For example, choosing $k=10$ gives an error rate of about one in a thousand, which seems rather high for most purposes; choosing $k=60$ means the expected number of errors would still be less than one even if you'd run the algorithm once a second since the big bang.