How long can I stay in Russia, as a tourist?

It depends on which country you are a national of. US citizens can, in some circumstances, obtain a tourist visa valid for up to 3 years and allowing a stay of up to 6 months per visit. For UK citizens a tourist visa is most often for a single visit or double entry, and allows you to spend up to 30 days in Russia in a single visit (e.g. dual entry would allow a maximum of 2×30 days).