To test the significance of a putative sequence homology. Keep the amino acid (or nucleotide) content constant, but swap around the residues randomly, and compute similarity again.
SWISS-PROT currently contains about 80.000 protein sequences. Select 1000 of these as a simple quick test set, before doing complete analysis. It is not good enough to use the first 1000 in the Swissprot file, since the entries have probably not been added in random order to the file.
Molecular dynamics: random initial velocities (Maxwell distribution for a given temperature), and maybe somewhat randomized initial positions.
An optimization algorithm to find the minimum (or maximum) of a complicated function. Use random numbers to explore many combinations of variable (parameter) values, and to decide which "bad" moves to accept during the search.
An optimization algorithm: Encode a proposed solution to a problem as a gene, allow mutations and recombinations randomly, perform evolution over a set of different solutions to find the minimum (or maximum) of the function.