Star Rise and Set Time Calculator
Here is a browser-based tool for calculating the rising and setting times of stars, the source code is available on GitHub. The code is based on formulae from various sources, with much credit to Barry Carter for his help and patience.
This tool does not take into account atmospheric refraction, which can affect rising/setting times by several minutes - if you need that kind of accuracy then see this page from the US Naval Observatory. The results have been checked against various other online tools, written by people far more competent than me, and they broadly agree, although each tool gives slightly different answers. It is probably safe to assume accuracy to within ±10 minutes.