To my knowledge they aren't capable of projecting force in a meaningful way outside their corner of the world, but on the other hand that corner is the largest around. I know they still wield influence on their member republics and even other states in the region no longer politically affiliated. Watch the headlines and occasionally even Washington has to compromise and court Moscow over small things.
I saw a decent Newsworld International report where they said that within Russia people back the Chechnya conflict because it 'arouses their fading sense of Russian empire'. I'm also remembering news like their caution to Azerbaijan against coopearating with the US military, their meddling in Georgia, and the games they have been playing lately over the Kyoto atmospheric treaty & Iraqi debt.
Add to this the ominously quasi-authoritarian election & events around it (more than quasi?) and I wonder where Russia sees themselves in the global 'big dog' hierarchy and what kind of role they are setting themselves up to play. What do you all think?