The C-5 can theoretically carry two M-1 Abrams tanks, but in practice is mostly going to only be able carry one over a long haul. The C-17 is also able to carry a single M-1. No other US airlifter is able to move them. However, that is a very expensive and inefficient way to move tanks, especially in the numbers used by a large armored formation. They were in fact almost entirely moved by sealift during Desert Storm. There were something like 4k armored vehicles moved as I recall, of which something less than half would have been actual main battle tanks. The logistical aspect of Desert Shield/Storm is actually one of the most impressive parts of the whole war, and one that gets far less than its due when it come to kudos.
In Operation Iraqi Freedom, we had quite a bit of pre-positioned stuff, and we also didn't bring nearly as many tanks. What we did fly in via airlift however was MRAPs, at least initially, because there was a strong outcry about all the casualties we were taking from IEDs, and a big push to get the troops something with more protection. Quite a few of the MRAPs were brought in via airlift due to the urgency, many of them on C-17s and C-5s, but from what I saw mostly on contracted Russian aircraft (ironically). If I remember correctly the C-5 could carry four of the larger MRAPs, the C-17 two, but the AN-124 could carry eight I think. We were getting a few AN-124s a day when I was the Director of Operations at Balad Airfield in 2007-2008 during the height of the surge.
