How Capable Is The Russian Military In Defending Russia And Deploying Around The World?

The Russian military is very capable of defending Russia. First, they have a seasoned corps of combat tested troops who are very good and second its a big, big country.
Second, just what are the threats?
The US? The US has its plate full in Iraq and Afghanistan and would never risk nuclear war. I know that the US is still the boogey man to some Russian radio hosts, but if the US doesn’t have the belly for that sort of war.
China? Relations are good right now, but the Chinese military is growing. However, it seems unlikely especially with growing commercial ties.
There could be friction with the Ukraine or some of the other FS states, but, as the case of Georgia shows, why poke the bear?
The biggest threat is from Islamic extremist in Southern Russia, but they are probably past high tide. However, this is not going away any time soon, at least not as long as oil powers the world economy.
There is always the possibility of internal issues, but those are more political than military.
So, given the threats, it is obvious that the Russian military is more than capable of homeland defense.
As far as projecting force around the world Russia is not in the same league as the US individually or the NATO countries as a group, but it is capable of sending and supporting its forces almost anywhere depending on the situation. In fact, other than the US and NATO, no other country is AS capable of force projection as Russia.

Well, for this short analysis of Russia’s defense and power projection capabilities we need to look at their equipment and their record of recent operations.
Air Force. Russian tactical aircraft are decent, but pilots are consistently hamstrung by a lock of funds. Up until this year, things improved and Russia has started flying long-range TU-95 patrols in the Pacific and North Sea. However, the Russian Air Force has had very little combat experience since the end of the Cold War. Their long range bombers and maritime patrol aircraft can provide a significant stand-off capability though.
Army. The army did well enough in Georgia last year, though I have read several articles that claims that man-for-man the Georgians fought much better than the Russians – they just ran out of units first. The Russian Army, even for elite regular units like paratroopers, has not been able to meet its goals for recruiting professional soldiers and reducing its dependence on conscripts. Alcoholism and abuse of recruits is still widespread and they still lack a truly professional NCO corps. That is their biggest shortfall in personnel management – and when you look at the other top-rate armies in the world, they all have mature professional NCO corps. Cash from oil and gas should allow Russia to upgrade its staple military equipment: tanks, IFVs, helicopters, etc., but they lack the heavy lift and global supply network like the US military that you need to operate large formations of troops outside your home territory. In Exercise Talisman Saber-2005, the US 501st Para Infantry flew nonstop from Alaska to NE Australia and dropped an entire brigade (I think it was that big) in the drop zone with only one injury. Russia does not have that capability. Its paratroopers that have fought in Chechnya walked/rode into battle.
Navy. The Russian Navy is a shadow of its former self and while they are reinvigorating their training, especially with their submarines, you are talking about a handful of vessels capable of full operations. The Russian Navy is still primarily focused to the West and its Far East Squadron is till only a handful of ships and submarines. The Russian Navy has also traditionally been one of the few Navies to have a real marine corps-like capability and while their Naval Infantry Regiments are well trained, they also have little experience in recent amphibious operations. Additionally, the Russian Navy lacks the amphibious lift and logistics capabilities of many western navies. The logistics problem still persists from the Cold War as Russia lacks a large fleet of oilers and still resupplies by going dead in the water while the US and all of its allies can resupply while making way. I have seen USN carriers resupply while launching aircraft. Finally, without a viable aircraft carrier, the Navy’s power projection is limited to the range of its strategic bombers. These aircraft can fly thousands of miles, but they are vulnerable to carrier launched fighters and would not have escorts capable of coming the whole way if they were to try to support the Russian fleet thousands of miles from home.
Russia has conducted several major exercises with China as well as within Russia. However, these are land-based and do not exercise true power projection capabilities. The access to domestic rail and road networks allows these exercises to take place, whereas the US military can move two brigades and two carrier battle groups to Australia for combined training as a routine operation.
Russia’s advantage is its long history of providing capable advisors and technicians. In their current iteration, there is no longer the political rhetoric of the Cold War and the government’s official position is often apolitical in regards to others’ political systems. This method allows them to project power on the cheap as other countries foot the bill. In the end, Russian interests are still advanced and the interests of competing nations in the same region are often thwarted. Therefore, I would conclude that the Russian military is still ground-centered with limited truly long-range power projection capabilities, but they are still capable of influencing others through their generous use of funds, provisions of advisors, and their willingness to send decent quality systems and missiles to anyone with the necessary cash.