PvP, Dungeons and Raids.
Or, just make another alt again and experience the same content from a different viewpoint.
No, you want to improve your "main" character. Some people are like that, myself included. Alts are nice and useful for a variety of things like farming, crafting, or just to have a backup in case one of your guild members is unable to show up and fulfill a critical role during the evening. Perhaps you enjoy trying different classes and making alts is simply the way you do it, or perhaps "leveling" is just giving you a better sense of character growth than replacing a few pieces of gear does.
Currently in WoW there's a distinct lack of ways to improve your main character. Yes I know, you can queue up for the dungeon finder until you reach a set cap of valor or heroism points, presuming you already got all the random drops that have a 10% drop chance and 2-3 others in your group are after as well... Of course the tank always leaves when the item "he" wants does not drop from the first or second boss in the instance, thus adding to your frustration.
Queueing for specific heroic dungeons is on a one day timer, and raids, well, let's not start on what a cock block those can be, right? Oh don't get me wrong, raids used to be great fun back when they were still difficult (During Vanilla and TBC that is), but right now you simply queue up for the random raid finder and hope you don't get stuck with complete idiots again like last week...
No, you want to improve your main character NOW. Character growth, improvement, get stronger, better and if possible BIGGER than the rest of the players. But, you're stuck at the level cap so questing won't do you much good, PvP is just another form of queue and random group that you may or may not succeed with. You prefer to SOLO.
So, achievements then. Is your achievement point total on 10.000+ yet? Did you run through every old dungeon and heroic for an extra 10-20 points? Loved and hugged some squirrels? What's the point in the end? Just a title, maybe a mount or a vanity pet, you can show off to your friends, or guild, not much more than that though.
Another approach is the looping in BvS or remorting in Dragon Tavern, this mechanic basically sets your character's level back to 1 and allows you to play the game again, while still keeping "most of" your previous skills. What's the point in that? Well, your character becomes stronger each time he or she reaches the level cap, thus eventually you have repeated that process a few times and levelling up again becomes more efficient.
Obviously that would be hard to balance in WoW, since not everyone has weeks and weeks to spend grinding up their levels indefinitely - it'd cause an outrage or two either way. But, it would also make the world more alive, players would be all over the world intead of just focused in the latest lvl 85-90 zone and lagging and annoying everyone in the area.
What sort of "perks" would make it worth levelling up from scratch that would not make it overpowered or excessively unfair towards other players. What would give you the sense of still growing stronger, without the fact of having done the loop/remort thing becoming a mandatory requirement for any guild member recruitment.
* Achievement points? Probably, but those alone won't make it worth the while.
* Titles? Oh come on now.
* Mounts? Not really. Mount speed? Yeah that might work - as long as it's normalized in PvP zones.
* Reduced fall damage as mentioned above for AA points.
* Customizeable armor colors? Could be worth doing, but wouldn't give you any sense of growth.
* Increased rested XP bonus speed, would make re-looping faster, thus allow you to level faster the next time.
Then how about: Reduced vendor prices, reduced armor repair cost, faster movement speed while dead. A lot of stuff that would not directly affect other players' chances of succeeding in PvP or raids. (Stuff that does affect PvP could be normalized or neutralized, same while in a raid zone).
Obviously, in order for a system as such to be feasible, all the quests you've completed while leveling from 1-85 should be re-set so you can do them again. But, would you do it? Would you enjoy doing it? Would you want to see other benefits added specifically to such a system?
Diablo 3 is getting a "Paragon" system which allows you to level up to +100 levels, much like AA points, see the battle.net post. Funny that.