In WoW and most other MMOs, the character is the central entity in the design around which everything revolves. But players have multiple characters. And there are a lot of game play elements which are fun the first time around, but are not so much fun the second time around.
The quintessential example here is reputation grinds. Working on rep is reasonably interesting on your first character. But it's excessive on your second character, especially if the reputation is necessary for endgame. Right now, WoW gets around this limitation by making important items Bind-on-Account, which allows you to transfer them to characters who don't have the necessary rep yet.
But, what if reputation was tied to the player account, not the character? Once you're exalted with the Argent Dawn, you're exalted on all your characters. You could have the long reputation grinds and chains once again, because a player only needs to do them once.
There are a lot of other elements which could be moved from the character to the player. Reputation, Achievements, Pet collections, and Mount collections are the straight-forward ones. But what about some less obvious elements?
Friends - We're already moving towards this with Real Id and Battletags. I predict that eventually the Friends Lists will exist at the account level, and consist of other accounts, rather than characters. Same thing with the Ignore List.
Gold - Gold could work at the player level. All your characters would have access to, and contribute to, a central gold stockpile.
Currencies - To extend gold, why not all currencies, including Valor and Honor points?
Inventory - This might sound a little odd, but does each character need a unique inventory? Could the same set of bags be used for all characters. There would be issues here, of course, but how necessarily unique are inventories?
Bank - A bank might work better at the player level, shared between all characters. Certainly would be easier than using the mail system all the time.
Guilds - There are probably a lot of objections to having players belonging to a guild, rather than individual characters. But there are also a lot of requests for being able to belong to multiple guilds at the same time. If we did have a multi-guild system, it certainly would be easier to have the account belong to the different guilds, rather than individual characters.
Attunements - I liked long attunement chains, especially for the first tier of content. But again, once you've unlocked something, it should be unlocked for all your characters.
PvP Matchmaker Ratings - Really, shouldn't a player's rating be consistent across all her characters? As far as I see, having ratings be character-based just allows people to game the system.
Areas like Molten Front - Similar to attunements, areas like the Molten Front would be better if you only needed to unlock it once. You could even make the process longer and more intricate, confident that each player only needs to do it once.
Lockouts - Possibly the most controversial element I can think of. But consider the idea of having 2 lockouts per account per week. You could do two raids on the same character, or raid with two different characters. There are also some shenanigans with alts at the very high end which this might cut down on.
When we look at the original design of most modern MMOs, almost all gameplay elements are unique to each character that is created. But I think that perhaps a better design might see the player as the central element, with all her characters sharing many elements.