* Normal dungeons (as they are now)
* Heroic dungeons (as they are now; meant as the first step of gearing up)
* Nightmare dungeons (as hard as Challenge Modes are, without any of the timing/leaderboards/scaling, that drop epic loot and/or points and tokens to buy epic loot)
But wait, you say: That's just trading raids for dungeons, and you have three versions of the same dungeon now instead. True, although I imagine there would be certain Nightmare-only dungeons in this situation, and a 4-5 boss dungeon is infinitely better to do on different modes than a 12 boss raid.
In this sort of game, your raids would still exist but they would be much closer to raids like Onyxia, Obsidium Sanctum, Throne of the Four Winds (minus the BS random loot, of course) and the world bosses than your huge Molten Core or Ulduar style raids. Raids become supplemental, dropping loot that's the same level as the Nightmare dungeons.
The key in this sort of system is to limit gear inflation, so everyone is always kept roughly around the same overall level, with the better players having more of the high-end gear at any given time. So for your "tiers" you either add in different currency (similar to the old badge system in Wrath), and you can add in additional Nightmare dungeons (T2 dungeons or whatever) but provide a reason to continue to run the original ones as well. Raids are few and far between, and are always parallel to the current Nightmare dungeons, instead of being on a curve at the top.