This gravitation of countries towards NATO is going to continue until countries stop viewing Russia as a threat, justified or not. I know Russians are not going to like the sound of this at all, but Russia is going to have to stop treating her neighbours as potential spheres of influence, and start treating them as sovereign nations with independent aspirations.. in other words - as equals.
The more Russia "responds" to the feeling of being closed in by NATO, the more her neighbours are going to want to join NATO. It seems like a bit of a catch22, but Russia is not going to get anywhere by trying to pressure countries to stop joining such alliances. The more Russia does this - the more countries will be convinced that joining such alliances is in their best interests.
Unfortunately (or fortunately, depending on how you look at it), the best thing Russia can do is stop trying to act like a superpower with sphere of influence interests, and start acting like a country willing to be an equal and a partner to her neighbours. Right now there is a lot of a "cold war" like feel to the proceedings, which is of course pushing countries into a "Maybe we should join NATO" corner. Russia can't reverse this with threats - that is just going to have the opposite effect. Russia can't really reverse it no matter what it does - a lot of the damage has already been done. The only thing left to do is chill the hell out and sit back, and build positive relationships with surrounding nations - instead of negative ones. It will take a lot of time, maybe decades, but eventually countries will chill out, once they stop seeing Russia as a threat. Justified or not, right now a lot of them do. Nothing really Russia can do, there is no magic bullet solution. You reap what you sow, in a way.