Russia (or rather its leadership) genuinely feels threatened by NATO and US, and it is a well-known fact that attack is the best form of defense. This is what Russia is doing now, even though in my personal opinion, they went a bit too far in this current Georgia crisis. Russia has a historical paranoid fear of invasions which from time to time was justified. WW2 only strengthened this fear. During the Cold War, while the West had trouble sleeping fearing a Soviet attack, the Soviet leadership was actually totally convinced (and possibly not without grounds) that given the opportunity NATO would attack first. So much of the Cold War was about making sure that there is a protective buffer between Russia and its potential enemies. Whenever there was a danger that a piece of this buffer would fall out, Russia acted swiftly and brutally (GDR'53, Hungary'56, Czechoslovakia'68, Afghanistan'79).
After the collapse of USSR, Russia settled for a status quo where there was still a narrow buffer separating Russia from the West. Moreover, in the 90's Bill Clinton even promised at some point that NATO wouldn't enlarge to include ex-Soviet states. However after the expansion into the Baltics, Russia got nervous, now threatened with expansion into Ukraine and Georgia, it is genuinely alarmed, and its leadership felt that they need to make a move. Moreover, the prospect of a US Anti-Missile defense system right next door isn't making things better.
Surrounded by US-allied Ukraine, Baltics and Georgia, Russia would indeed be extremely vulnerable to a hypothetical conventional attack. Russia's conventional forces are in a dire situation, so even no nuclear attack would be needed to completely disable the European part of the country. So I totally understand why the leadership is alarmed. With US airbases in Ukraine, say, even a limited air campaign (for example to force "regime change") against Russia would be devastating.
I think what the West has to do is to stop exarcebating the situation by making new threats to Russia, but rather address the old threats, and agree on some compromises. If they say that NATO is not aimed against Russia, then who is it aimed against? Terrorists from Afghanistan? Well, I doubt Ukraine or Georgia need protection from them.
Further threats and further isolation of Russia will just make it even more aggressive, and this will be a vicious circle. If the West wants to claim the high moral ground in this, they need to make the first move to stop the escalation. Crisis talks have to be held with Russia to discuss not each problem separately - Georgia, Missile defense, Ukraine, but everything together to try and pinpoint what can be done to normalise the situation. Clearly the current post-Cold War security arrangements in Europe are now inadequate. Compromises have to be made on both sides.
One way out (or maybe forward) that I see, is to invite Russia into NATO, together with all the other former Soviet republics. This would require some change on part of NATO, and change on the part of Russia, but to avoid further potential conflict in Europe, I see this as one of the best solutions. If Russia is part of NATO, it won't have to be afraid of a potential NATO attack, and the border between Russia and Ukraine won't be a border between NATO and a potentially hostile country. Such a move would also make Russian generals sleep better at night. I'm sure some of them have nightmares of millions of Chinese soldiers crossing the border in the Far East!