Take a break if you want
While it might seem ridiculous to extend your love of WoW by taking a break, enjoying some time away from the game can do wonders to refresh you. The parts of the game that feel like chores will stop being so onerous, and when you do come back to WoW, the whole thing might feel renewed again.
Taking a break also lets you get away from another source of burnout: people. Sometimes, you can burn out by dealing with folks in the game as much as anything about the game itself. Taking a few months away can definitely help you feel more comfortable when you return.
You should be careful to gauge how long you actually want to be out of game. Sure, you could just wait until it feels right to return, but we might all be playing pandas by the time you come back around. Set a few milestones for yourself so that you know when to come back and test those Azerothian waters.
Pick up a new class
It seems like new characters grow up to level 85 as quickly as you can run across the starting zone. That being said, there's a huge difference between leveling a new character and really playing a new character.
Take the time to do some dungeons, run through some heroic groups, and even explore the raid content. Playing WoW as different roles makes it feel like a different game altogether. The experience of fighting a raid boss as a melee character is much different than frantically trying to keep the raid healed.
Finish up some achievements
Achievements are a huge part of the game. We do have an entire column dedicated to them, after all. Take a look at your achievement list and see if that looks like an attractive list of goals.
The nice thing about achievements is that you can solo the vast majority. At level 85, in contemporary gear, you'll have no problem handling most of the old content on your own. For that matter, you can find PUG groups for most stuff nowadays. Firelands PUGs are perfectly capable of handling even Ragnaros at this point.
Build your transmogrification set
In patch 4.3 (which could be only a few weeks away) includes a new feature called transmogrification. You'll be able to switch the way your armor looks. If you're truly bored out of your skull, now's the time to go back and grab your transmogrification gear.
You can grab your transmogrification set later, of course, but a lot of your aesthetic gear still relies on a random drop. It's possible you could start trying to get it now yet still have not seen the gear drop by the time we're all suiting up our Pandaren.
Try different aspects of the game
If you usually focus on PVE, give PVP and roleplay a chance. Conversely, if you're an Arena junkie, maybe you should give raiding a shot. It's all about switching up the game and trying out new things. After all, WoW really is a massive game. Maybe a change of pace is all you need.
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.