I don't have much to add to the know how or reasons of why a Carriers won't be obsolete any time soon. As others have stated, destroying one would be difficult at best, and impossible for many nations entirely. Are they invincible? No, absolutely not. Will tech be created that counters them? Sure, someday.
However, to everyone commenting that armies are built based on the last war, that ignores the fact that the only nation on Earth that has been in a perpetual state of war for nearly its entire existence is the US (whether we call War or not). Since WWII, the US has been involved in one armed conflict or another almost in perpetuity, and the military has been evolving to meet those needs. The fact is that the world views us as a global peacekeeping force for them (barring the dozen or so nations who either want chaos, or want the power the US has). Yes, they complain (looking at you France), but when a problem arises, they usually ask the US for military aid (again looking at you France). That means the military and its components (such as Carriers) have continued to advance and evolve both offensively and defensively to be better protect against incoming attacks, and better destroy what is making those attacks. Again, that doesn't make it invincible, but it does mean that we are less likely to fall into the 'last war' trap.
Personally, the only thing I think could make a carrier partially obsolete would be something like the Tuatha de Dannan from Full Metal Panic. A submersible aircraft carrier capable of reaching targets and launching planes with speed to submerge and escape would be invaluable because it would be nearly impossible to track. That or a space laser a la Hammer of Dawn from Gears of War, but last I checked that doesn't exist except in Bond movies and other sci-fi works.