I tend to think that MBTs will stay around for a while to come. The analogy made to battleships at the end WWII may be valid. However, if it is a valid comparison, the tactical siutation for MBTs today is not entirely similar to that faced by battleships at the end of WWII.
Opponents
At the start of WWII, we needed battlewagons to defend against the other guy's battlewagons, but after WWII, there were no more battleships to fight. Our potential iron curtain opponents weren't deploying them, so our own need for the diminished.
On the other hand, currently many of our likely opponents have very competant MBTs, so we need to have a counter. Presumably a Bradley equipped with an anti-tank missle has a good chance against an enemy MBT provided that they get the jump on the enemy, but I don't think that anyone really wants to make that matchup part of the Bradley's bread-and-butter operations.
Targets
At the end of WWII, battleships no longer had much in the way of likely targets. Naturally, there were no battleships to sqaure off against, and principle ship to ship fleet action would be handled by carrier borne aircraft and submarines. The only real targets left for battleships would be shore facilities, primarily as part of pre-invasion preparation. The navy figured they could handle those tasks with aircraft, so battleships were retired because they were a very expensive luxury to handle a fairly limited role.
On the other hand, MBTs still have lots of battle field targets. Enemy MBTs, APC.s, pill boxes, strong points etc. Admittedly, any of these items can be taken out by a missile, but missiles are usually fairly expensive compared artillary rounds. Considering the number of such targets that need to be eliminated in a ground offensive, it probably adds up to make the tank not seem as expensive.
All in all, I think the Abrams has a place in the arsenal for a long time to come. With the changing nature of warfare, i.e. no more Kursks. possibly the next generation of MBT may well have its designed capabilites adjusted to account for the more likely scenarios of the future.