EDIT
Georgia does not have oil, but it is a transit country. This is valuable because it provides the only outlet for Caspian oil and natural gas which is not going either through Russia or through Iran. (See the maps and the wider context in that diary) And after a 15-year tug-of-war, the Baku-Tbilisi-Ceyhan pipeline was inaugurated two years ago: it takes roughly 1 million barrels per day from the Azeri oil fields run by BP to the Mediterranean coast of Turkey, via Georgia. That's over 1% of world production, and it is fully controlled by Western oil majors. There is also a smaller gas pipeline that follows the same route and brings smaller volumes of gas from Azerbaijan to Turkey.
These pipelines have been at the heart of the relationship between Georgia and the USA over the past 15 years, but, oddly enough, they have played a very small role in the current crisis. In fact, the BTC pipeline has been cut off for the past few days, not because of events in Georgia (which are in the north of the country, whereas the pipelines go through the south), but because of a bomb attack in Turkey before the conflict started, with claims by the PKK, the Kurdish movement.
The reason the current conflict is not about the oil is because, now that the pipeline is built, that game is, in effect, over. Now, the only thing that could stop the flow of oil is, other than localised attacks (like the one conducted by the Kurds, something that has long been expected, and which was mitigated by building the pipeline on a route that avoids kurdish territory) would be for Russia to actually invade all of Georgia and physically take control of the pipeline, ie an outright act of war not just against Georgia, but also against the US.
The reason for that is that, as part of the process to put in place the pipeline, Georgia invited the US military to set up a base on its territory, near the route of the pipeline. Thus, any attack on the pipeline by Russia would become an attack on the USA.
EDIT
http://www.energybulletin.net/node/46173