Although you specifically titled your thread about warriors I though I'd come in here and add my thoughts on Paladins too.
It used to be the case prior to Wrath that mana was sometimes a problem for Paladin tanks, even with a little intellect stacked back then my pull spell would eat up a huge amount of my mana pool before we've even got the pull underway properly. If you were overgeared for the instance, or once you have raiding gear and you were running normal instances say, then you'd have to stop to drink after virtually every pull as you were just not taking enough damage to be healed enough to gain mana back effectively. This also applied to heroics for those tanks in T6 gear, though to a lesser extent.
What used to happen and yes I myself have done this, is if it was relatively safe to do so, I'd sit down mid pull very quickly eat a crit so I took more damage and thus got healed. Doing this too often made healers quite unhappy and wasn't really the best or most efficient use of the healers time.
The thing is though in "on-level" content where we were taking plenty of damage we'd finish with a full mana bar as we took a lot of healing over the length of each pull. This, from my perspective, made running friends through low level dungeons more of a chore than heroics.
Fast forward to now:
Blizzard in their infinite wisdom decided that Paladin tanks should not have to worry about mana while tanking. They decided to remove all Intellect from our gear to the extent that now I have nothing other than a white intellect value. They gave us new tools to recover mana:
Blessing of Sanctuary, gives us 2% of our mana pool back each time we dodge, parry or block an attack, which with a decent geared tank is pretty much 100% of the time. With little need of CC at the moment and with several mobs beating on us that tool alone gives us a huge amount of mana back each time they take a swing at us.
We still have Seal of Wisdom and now an independent Judgement for it too regardless of our chosen Seal.
Divine Plea, new spell not just useful for the Paladin healers, 25% of our maximum mana back over time.
Spiritual Attunement and its associated Glyph.
In short they pretty much removed mana from the table. It is still a small issue if I'm off tanking in raid, but if I run low I'll pop Divine Plea, or judge Wisdom but I rarely run out. In 5 mans as threat is no longer an issue - we can virtually auto-attack and keep aggro - alot of tanks are judging Wisdom anyway on standard pulls, with the changes to threat and judging Light in the upcoming patch you can expect more to be using Wisdom too.
The fact is now I'm in a lot of Naxx gear (10/25) I still use up a fair amount of mana in smaller heroic pulls/normal dungeons, however in those cases Shielding me shouldn't be necessary. In the larger pulls, boss fights or against casters I'm still going to be taking enough damage that even with a shield up alot of the time I'm more than capable of recovering mana from the many tools we were given for that very purpose.