They say you can never go home again. They don't really mention whether you can return to old dungeons. Blizzard hopes you can, and will try to tempt you back with the upcoming 6.2 patch. It's set to add a new event type: Timewalking.
"In Patch 6.2, we’re introducing seven different weekend events that will run from noon Friday through noon Monday every week," writes Blizzard (opens in new tab). "Two of those events will be Timewalking weekends, in which you’ll be able to queue up for a randomly selected old-school dungeon with a new sort of “heroic” difficulty."
When you're doing the Timewalk, your character's power and gear will be scaled down. "For the first time in years," writes Blizzard, "some dungeons you outgrew long ago will once more put your skills to the test."
Naturally, there'd be no point in any of this is the loot wasn't scaled up in response. Blizzard uses the example of King Ymiron's Red Sword of Courage—obtained by completing Utgarde Pinnacle—and say it will "scale up to an item level appropriate for use at your level".
Timewalk events will be available from level 71 for Burning Crusade dungeons, and level 81 for Wrath of the Lich King dungeons.