Nope, it won't be another Georgia. This is a recurring tragi-comedy caused by a messy snarl of conflicting interests and interest groups.
First, natural gas is an unusual commodity, because it's delivered by pipeline and can't be effectively transported far from those lines. That means that both the buyer and the seller are in a monopoly position -- if the buyer won't buy the seller will find it hard to sell the gas elsewhere, and if the seller won't sell, the buyer won't be able to buy it elsewhere either. This means that gas prices are not set by competitive markets, but by bilateral negotiations between the seller and the buyer. This process looks a lot like a game of chicken.
Second, Russia has been selling gas to Ukraine for much less than it charges for EU countries, for a number of reasons: because Ukraine is dirt poor and can't afford to pay more, and because the pipeline runs through Ukraine and Ukraine can just steal gas destined for Europe. So, Ukraine can deny Russia profits from the more expensive gas going to Europe, and Russia can deny Ukraine the gas it desperately needs.
So what we're seeing here is a round in that game of chicken. It obviously always happens in early winter, because that's when Ukraine and Europe need the gas most; Russia threatening to cut off supplies in July wouldn't cause much of a row.
A salient point is that the Russia/Ukraine gas deal is renegotiated every year.
So, what happened just now was that Russia wanted to hike the price of gas for Ukraine by a fairly hefty amount in the 2009 contract (still leaving it much below what it charges Europe). Ukraine said "No." Russia said "OK, we'll cut the supplies then." Ukraine said "Try me." Russia did, and now Ukraine, Turkey, Bulgaria, Romania, Hungary, and Greece are out of gas. Now it's a matter of waiting to see who blinks first.
Now, another question is *why* Russia wanted to raise the price of gas just now, and why it didn't blink yet. There are a number of reasons for it.
The obvious one is that the fall in oil price has left a huge hole in the Russian budget, which they're looking to patch in any way possible: raising the price of gas that you know your customers need and can't get anywhere else looks like a bit of a no-brainer from that point of view.
There are other, less straightforward ones too. Putin and Medvedev have no love lost with the Ukrainian prez, Yushchenko, ever since he won out over Kremlin's man Yanukovych, back when there was all that fuss about the orange flags and stuff. Now, it appears that the PM, the blonde lady with the Princess Leia hairdo, Yuliya Tymoshenko, may be attempting a power play against him, and there's suspicion that she's cut a deal with the Kremlin about this: the Russians make the Ukrainians freeze for a while, they get upset at the Prez, Tymoshenko steps in, and magically the gas starts flowing again: everybody's happy, except Yushchenko, of course. (The thing to keep in mind is that Ukraine is incredibly corrupt; these guys are all crooks, and some of them are actual murderers.)
Yet another point is that Russia wants to build another gas pipeline in the Baltic Sea. The Germans are for it, but many other EU countries are against it. So, if Russia can make the Ukrainian pipeline look like a bad risk, they're hoping to turn around the opposing EU countries so the Baltic Sea pipeline can go ahead. (I'll be damned if I understand how a pipeline in the Baltic Sea will help get gas to Greece, though.)
So, it's basically a bunch of regularly recurring arm-twisting based on money, power, and people cordially despising each other. However, I'm really not too worried about this spinning out of control. Russia has its hands full with its own problems right now, and isn't about to get into a serious scrap with Ukraine; Ukraine is behaving like Ukraine usually does, and the folks in Southern Europe will have to wear a few more sweaters for a while. The Ukrainians will have a very unpleasant winter, but then again they usually do. I'd expect it to sort itself out in a couple more weeks.