Yes, that's right. My JC alt was a level 70 warrior. And now, he's a level 76 warrior. And I'm having a blast seeing all the stuff I've already seen four or five times now (depending on if you count my Horde alts and taking into account that they have different quests to some degree) on a class I've already leveled to 80 twice. (I also leveled my draenei warrior to 76 before abandoning him.) To be honest, part of it is the fun of trying out a fury spec designed entirely around as much self healing as possible with the Glyph of Bloodthirst and Blood Craze, and part of it is just that I missed these particular questlines.
I really like questing through Howling Fjord. Sure, it would make more sense to do it on a different class, but I already leveled two shamans, a DK and a paladin through these zones. Why not go back to a warrior? After all, we all know I like warriors and I'm completely freaking insane, and I'm enjoying tweaking the self-healing build for minimum down time. (I also made sure to get the healing trinket from the Wrathgate questlines to ensure as much self healing as I could.)
I won't pretend that I'm not also taking advantage of heirloom shoulders, chestplate and a weapon: I'm not an entire masochist. Still, I'm really enjoying what I'm doing, surprisingly so. It's fun to see all those quest NPC's again, the ones I have no reason to visit on my main. It's fun to level a new profession (I also picked up inscription on my DK this month, so I'm rapidly turning into a one stop shop for my main's raiding needs) and to find those quests I managed to miss the first time.
So I turn again to you: do you like leveling alts? Are you enjoying your climb through the zones of Northrend, or even Outland or old Azeroth?