I found that mapping slowed things down.
Nowadays, I try to justify a way to give the players a map in the game (perhaps the first corpse they find in the dungeon has a map).
The map is always a hand-copied version of the DM's map, sans hidden stuff, and drawn out of scale such that the players generally, know which rooms to goto (which is what really speeds up game play), but they won't be immediately able to deduce where the secrets are.
I figure, the party has a wizard or some high INT character. They may not be physically mapping, but somebody that smart probably has an eye for details and isn't too likely to get lost (you don't get lost in a new building your visiting do you?). Basically I find an in game reason to justify making game play faster and easier.
I find things go really quickly when the players can point at the map and say, "we're here, we want to go here, by this path" and I can then describe what happens.
Real examples:
I ran a 4 level dungeon for the party. In 6 hours, they got to level 2, when I made them do all the mapping by hand. The next session, I gave them a map and they cleared the remaining 2 levels in 3 hours.
The last session my friend ran (as a new DM), he gave us a hand drawn map (nice prop actually). The game ran from 6PM to 9:30PM. We introduced the party, got the plot hook, and cleared 5 combat encounters in that time span. Having a map (and a time limit because we had to work early the next morning) made the game play faster.
Janx