Instead, aircraft carriers use the C-2 Greyhound, and adaptation of the E-2 Hawkeye carrier based command and control plane, to make air cargo deliveries on and off an aircraft carrier. The C-2 design was introduced in 1966, with purchases made 1984-1990 and about three dozen of them remain in service. Current plans call for the C-2 to remain in service until 2015, and with refurbishment and enhancements, perhaps as late as 2027.
One wonders, however, if the C-27J, recently adopted by the Air Force and Army as a mini-C-130 couldn't be adapted for Naval use. A U.S. aircraft carrier has about 1,000 feet in length, which while less than the 2,000-2,500 feet the C-27J is billed as being able to handle, is much more plausible as a possibility than it was for the C-130.
On the other hand, the MV-22 Osprey has about the same cargo capacity as the C-2, and can much more easily handle the short runway of a carrier, so it would be a more obvious replacement for the C-2 (and perhaps the E-2 as well). The MV-22's Department of Navy predigree and planned use on a variety of Marine ships also makes it a more natural replacement from a bureaucratic perspective.
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As footnote another carrier based aircraft, the S-3, originally created for anti-submarine warfare, will probably be phased out and not replaced in 2009.
Although the US Navy S-3 obtained the S-3 strictly as an ASW aircraft, the service found such a "flying truck" to be very useful, so much so that the Viking was sometimes called the "Swiss Army Knife". However, despite its usefulness, the future of the S-3 is somewhat uncertain.
The main problem is that the aircraft are all getting old, meaning not only that they are becoming less reliable but that their systems are becoming too far behind the times. . . . The Navy is considering a WSIP II modernization effort, which would involve "service-life extension program (SLEP)" to provide selective structural improvements to S-3 airframes, in hopes of keeping them in service until 2015 at earliest. . . . The Navy did consider a replacement, the "Common Support Aircraft (CSA)", which was to be in the same size and class as the S-3 series. While the Viking had been designed as a dedicated ASW aircraft and was adapted to a wide range of roles, the CSA was to be designed from the outset as a multirole machine, performing such duties as ocean patrol, antisubmarine warfare, airborne early warning, carrier onboard delivery, SIGINT, and so on. However, the Navy also had higher-priority programs, such as the F/A-18E/F Super Hornet fighter; the F-35 Joint Strike Fighter; and the Boeing 737-based Multimission Maritime Aircraft (MMA) to replace the P-3C Orion [Ed. the MMA became the P-8 and will be purchased]. There simply wasn't enough money available to fund the CSA as well; the CSA program was shelved and it is unclear if it will ever be revived.
The Super Hornet is far superior to the Viking for the strike and tanker roles, providing better performance and load capability with state-of-the-art avionics, and the ASW mission is seen as of declining performance in an era of "brushfire" wars. The Navy seems to believe that the E-2C Hawkeye will not need replacement in the AEW role, or more specifically that old Hawkeyes will be replaced by new Hawkeyes, and so the only outstanding mission left to worry about is the COD role. What really complicates the matter is that at present the Navy is also considering the possibilities of unmanned aerial vehicle (UAV) technology to complement or partly replace manned aircraft.
Wikipedia adds a bit more detail to the S-3 prospects:
Starting in 1991, some of these were upgraded to the S-3B with a number of new sensors, avionics, and weapons systems, including the capability to launch the AGM-84 Harpoon anti-ship missile. The S-3B can also be fitted with "buddy stores" external fuel tanks that allow the Viking to refuel other aircraft. . .
Since the submarine threat has been perceived as reduced, the Vikings have had the majority of their antisubmarine warfare equipment removed and are now used primarily for sea surface search, sea and ground attack, over-the-horizon targeting, and aircraft refueling. As a result, crews are now usually limited to two, though three person crews are not unusual with certain missions. It has been used as a jet VIP transport, as was the case of bringing George W. Bush aboard the Abraham Lincoln.
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The current Navy plans call for the retirement of all Vikings by 2009 so new aircraft can be introducted to recapitalize the aging fleet inventory. Their missions will be spread among the other battlegroup fixed-wing and rotary-wing aircraft.
The ES-3A electronic intelligence version of the S-3 was in service from 1991-1999 but wore out quickly due to heavy use and had range issues. A small number were converted for cargo duty and used in that way. A tanker version was abandoned before being introduced.