Russian definitely has dialects with pronounciation specifics (e.g. one can differ south accent, as mine, from Moscow one), but at least among cities language is very "smoothed" due to huge migrations, radio and TV influence. Experts can differ urban dialects for hundreds of properties, but most of them aren't detectable by person without special education. Nowadays one can hear original dialects with full their specifics only in villages.

Some examples of original differences:

http://www.gramota.ru/book/village/map14.html - type of "g" (explosive, fricative)

http://www.gramota.ru/book/village/map15.html - type of "v" before consonants or at word end (labiodental or bilabial)

Sentense intonation is almost equal for most Russian dialects in sense that in simple sentenses only one logically stressed word has changed tone of stressed syllable. Complex sentenses with subordinate clauses get smoothed intonation floating. (The notable exception is Olonets region which keeps some reflects of old tonal stress system.) The same is true for east Ukrainian dialects, as opposed to west ones, where intonations are closer to common European style (the bound is approximately between Ternopil and Zhytomir). So, if you want to hear sentense intonation style known in English, German, etc., study west Ukrainian dialects:)