What’s the cheapest way to send money from the U.S. to Russia?

If you do not want to get hit on the exchange rates, a bank wire transfer would be the most safest and economical method to transfer funds. If the funds int he recipient bank are showing up in native currency and not US$, then it would be a good idea to ascertain at what rate would your bank settle the exchange rate at? (usually it would be 0.5% or less than the official interbank rate).