Blabberwort posted on the official forums with an interesting suggestion: Create a new dungeon setting that allows players to explore dungeons on a lower level of difficulty. According to the poster, this "Tourist" setting (as opposed to "Heroic") would allow curious players to experience the content although they wouldn't be able to earn any loot from killing creatures in the dungeons. For many players, this would likely satisfy their raiding urges, since it seems that a lot of non-raiders would simply like to experience the content once or twice without the pressure to continually farm it for loot.
Prior to the expansion, I didn't have a lot of opportunities to raid and a similar idea occurred to me. At the time I thought it would be pretty cool if there was a quest for each major raid dungeon that gave the player the chance to explore it without being able to engage in combat with any of the creatures. For instance, at the end of a lengthy quest line throughout Blackrock Mountain and the surrounding zones, you're finally tasked with a reconnaissance mission into the heart of Ragnaros's lair. You'd be able to enter the zone just like normal, but when you arrived inside the Core, you'd be wearing a non-removable Dark Iron dwarf costume. All the creatures would be friendly to you and you could talk to them as you made your way through the dungeon, completing the requirements of your quest. (Check out the quest "Who Are They?" for an example of what I'm talking about.) Perhaps you'd have to deliver a message to one of the bosses or simply visit certain locations in the dungeon, but the quest would have a definite objective and ending. If you chose not to complete the quest, you could keep it in your log and continually explore the zone.