Having been reading this thread with interest, some thoughts and observations have occurred to me.
For those who wonder why (or have complained about) the scenario almost always being the sinking of a USN carrier, that is because roughly half of all aircraft carriers (approximately 22 active worldwide) begin with their names with USS. Also the US carriers are amongst the most active in terms of operations, as opposed to carrier ops conducted by other navies such as Brazil and Thailand. By way of example, IIRC the Thai CVS carrier Chakri Naruebt is used more as a royal yacht and does not usually put out to sea with its full air group of six Harriers and six Seahawks.
In terms of methods suggested, so far a number have been mentioned which can sink a carrier, however none seem likely to do so. It seems that what GF and others have mentioned about factors that need to be considered when engaging a USN CBG/CTF has not been fully realized.
As I see it, the following events need to occur (more of less in order) to successfully sink/mission kill a US carrier or its associated Task Force/Battlegroup.
First the attacking force needs to get data on the location of the CBG of sufficient quality to allow it to be targeted, with the type and level of quality dependent on what method(s) will be used to actually conduct the attack. Additionally, when the data is gathered, it needs to be done in a manner in which either the US is ignorant of or unable to do anything about.
Secondly, the attacking force needs to get into the proper position to launch the attack. The requirements on the position would similarly to the above be dependent on what the method(s) of attack would be (eg AShM, AShBM, mine warfare, torpedoes, etc).
Thirdly, while the attacking force is being positioned, the ISR resources of the US need to be either destroyed, neutralized or evaded sufficiently so that US defences cannot prevent the attack.
Fourth, the attack needs to be actually carried out, in the face of potential
US reprisals.
Of the four overall items mentioned, the last two seem to be the most disregarded.
In terms of the US ISR resources, not just those of the CBG are of concerns. Rather the whole range of US government ISR, covering land, air, sea, undersea and space-based assets need to foiled in one manner or another. Given the capabilities of the various ISR systems and wide range of methods that covers, particularly when compared to other nations, that is a very difficult task. To illustrate what I mean consider the following.
Some nation decides to carry out an attack on a USN CBG and then starts drawing up plans to do so. As a result of normal comm intercepts, the US learns of the country's plan to launch an attack. As a result, the US changes the composition of the CBG, or the location, or the vector to give the US favourable results, or just conducts a premptive action of some sort to deny the hostile country an opportunity or the capability to attack. Alternately, the US might notice the movement or massing of forces that could conceivably carry out an attack on a CBG or other valuable target and the US could again respond or prempt accordingly.
Regarding the last item, it must be remembered that such an attack would not occur in a vacuum. If the US was not already at war with the country launching such an attack, they immediately would be. Then the attacking country could fall under attack from the full range of US military capabilities. Given that the USAF seems to have the ability to hit targets anywhere in the world pretty much at will, that is a potentially enormous disincentive to trying to sink a US carrier. On the other hand, if the US was already in a state of war with the attacking country, then there would be degradation on the part of the attacking country in capability to carry out the first three parts mentioned above needed to launch the attack.
I would suggest that the USN, long an operator of carriers, has experience in what is needed to keep the vessels safe. Similarly, the US has a general edge over other nations in terms of technology. This, coupled with the tactics and practices developed over time and through experience would make an effective attack a difficult prospect. I would further suggest before recommendations are made on weapons used or deployment methods, consideration be given to how the US ISR apparatus could be successfully bypassed since if that is not achieved the attack would likely fail before it even began.
-Cheers