Finish your quests. The new Cataclysm options give you a lot of choice while you're leveling. Most folks skip either Hyjal or Vashj'ir, for example. Now that you've achieved the max level, you can go back and do those areas. There's a lot of lore and fun to be had in all the Cataclysm zones, and you shouldn't miss it. You probably even haven't finished Twilight Highlands or Uldum, and those zones are spectacular.
Do low-level content. In the same way you probably skipped some of the Cataclysm content in your journey to level 85, you almost definitely missed a lot of the non-Cataclysm content. Wrestling through those zones is a shared experience that provide a lot of camaraderie among WoW players. Take the time and try the other racial starting areas and visit all the zones you never saw.
Gear up for heroics. New level 85 characters have a lot of gearing up to do before they hit heroics or raids. While you can take some shortcuts on the way to that level of gear, the process itself can be fun.
Tackle Tol Barad. The new world PvP zone is Tol Barad, and winning it isn't necessarily easy. The zone has a lot of quests for winners and losers alike, with a lot of achievements to people who are dedicated to fully mastering Tol Barad.
Build your reputations. Just like Wrath before it, Cataclysm has reputations that let you buy epic gear. There are even addons to help you out. As you tear up the heroics to build your gear, you can also grow your reputations at the same time.
Become a PvP legend. There's more to becoming a PvP legend than just entering Tol Barad. Mastering the art of player versus player content takes time, dedication, and a lot of deaths along the way. It can be a frustrating road to travel, but dominating PvP can be one of the most rewarding parts of the game.
Finish off your professions. Level 85 characters frequently never get to max level in their professions. That's because it takes time ... time you now have, since you're level 85. Once you've finished off your professions, you can turn those skills into gold by selling your products on the auction house.
Learn to raid. Raiding endgame content is one of the assumed goals of hitting level 85. Raids have been more growing increasingly accessible, and you should be able to find 10-man groups by asking around your official forums. Browse our Ready Check column to get an idea of what will be expected of you.
Try out some alts. WoW is darn nearly a different game for each class you play. If you find yourself getting a little bored and you want to try something new, fire up a new character. Changing factions, races, and even something as minute as your spec can bring you a whole new experience.
Experiment with roleplay. If you've never roleplayed before, you can quickly find out that all the World of Warcraft's a stage. Roleplay can expose you to a whole different kind of game in which you take on the role of your character and write your own story. It's an engaging and exciting experience and will help you get the most out of an escapist experience.
Visit the WoW Rookie Guide for links to everything you need to get started as a new player, from how to control your character and camera angles when you're just starting out, to learning how to tank, getting up to speed for heroics and even how to win Tol Barad.