An excellent question:-)
As I have the most experience with Poles and Russians, I'd prefer to confine my answer to those.
Russians typically sound much like a viscous river, slowly oozing along. Owing to extensive palatalization, often the Russian speaker gives the impression of a guarded, cautious, sometimes "lazy" accent, compared say, with the Pole, who can give the cursory aural impression of an exploding fire cracker:-)
Poles have far less palatalization than the Russians, often with a sort of chirpy speech, lending a sometimes excitable-sounding character to their conversation, even if this may not be so at all.
Thank you Lyzhko!
How would you tell unpleasant and weird Russian accent sounds to the native English speakers in general? I've read different opinions on this regard ranging from "very sexy" (especially when spoken by a woman) to "mafia like" and "chilling to the bones" (especially when spoken by a man). Many Russians find Georgian accent unpleasant (and other trans-Caucasus accents). While Baltic people or say Italians speak Russian more pleasantly. Well, I guess everyone supposed to hear Putin or other Russian top officials speaking English on TV.
All such "labels" in the end are meaningless, Vlad!
Any manner of speaking is subject to purely subjective impressions; Germans sound "harsh", Poles sound "sexy", Russians sound "lazy", Italians sound "hot" etc..
Any group brings its own social and cultural values to bear upon their speech. It's more what WE impute to the accents of foreigners than the reality of what they are really like.