Eric at The Dragon's Flagon has a great post about movement rates that says most of what needs to be said. I'm going to go through some brief experiments I did and the results I got, and extrapolate that to a reasonable table of movement rates for exploration movement (i.e. movement through a dungeon, or other dangerous locale).
D&D standard movement rates have people walking at .13 mph. That's 4% of normal walking speed. At that rate, it would take me ~3 minutes to walk to the next room to get a glass of water (a distance of about 36'). Actual time: 8 seconds. To account for the fact that you're not strolling through the park, I tried walking to the kitchen carefully - checking corners, listening at doorways, inspecting everything on the way, moving on the balls of my feet, etc. etc. and the actual time was 15 seconds.
Recap for Kitchen Trip Experiment:
D&D speed: 3 minutes (120'/turn, .13 mph)
Actual Speed: 8 seconds (2600'/turn, 3.1 mph)
Actual Speed (careful movement): 15 seconds (1400'/turn, 1.6 mph)
D&D exploration rates are TEN TIMES too slow.
Let's add mapping into the mix. I tried walking through the ground floor my house and making a detailed 5' square map of the place (distance covered about the same as the last example). I also did the same walk, but made only a ring-and-spoke map (i.e. corridors are lines, rooms are blobs, scale is not precise):
D&D speed: 3 minutes (120'/turn, .13 mph)
Detailed map: 61s, (350ft/turn, 1/2mph)
Ring-and-spoke map: 12s, (1800ft/turn, 2mph)
As I said in my comment on Eric's post, I think that the character's map would be more like a ring-and-spoke than a detailed scale map. In my mind, the scale map is to give the players and idea of what the space is like. The characters just need to know, "How do I get to the Chamber of 32 Doors? How do I get out again?". If your ideas differ from mine on that, that's fine - use the detailed mapping rate.
I will also note that, while doing the detailed map, I wasn't good for much else. I wasn't checking corners, I could have walked right by a secret door, or stepped on a pretty obvious pit trap. My assumption here is that there is a party of adventurers, and that they each have a role (point, rearguard, mapper, trap checker). If you're alone in the dungeon, I'd halve that rate (which actually get's back pretty close to the D&D rate). That said, I think mapping is the kind of thing that would get easier with practice. I could see an experienced mapper going up to twice as fast as me, or the same speed, but being twice as careful.
This is what I would say for a party of adventurers, under ideal conditions (i.e. decent light source, decent footing):
Base Rate: 2600'/turn
Exploration Rate: 1200'/turn
Detailed Mapping Rate: 600'/turn
Solo Mapping Rate: 300'/turn
Very, Very Careful Rate: 150'/turn
Edit: Eric at The Dragon's Flagon points out that the mapper could simply pace of distances, and remember them until the next time the party halts, and update the map while the party dickers or searches the room. I think that makes a lot of sense, and more or less obviates all but the base rate and the exploration rate.
Implications for Resource Management
So a standard torch burns for 3 turns. In normal D&D, that would mean 360' explored. As I see it, that would be good for 3600' explored. For perspective, that's enough to cross ~3 sheets of 5x5 graph paper the narrow way at 10' to the square. For the trip out, where you're just retracing your steps and not mapping, exploring, etc., it might be reasonable to say you could walk at the base rate, which means that 3 torches would get you across SIX pieces of graph paper, there and back, in a straight line.
If you check for wandering monsters, that means you'll be checking once for every ten checks you did under the old movement rules.
As Eric points out, what this adds up to is that it's pretty pointless to track time moving. It just doesn't take enough time to get around to make it worthwhile. Track time in the dungeon spent dickering about deciding what to do, time searching for that gem you know is in that pile of trash, or time spent looting the bodies after a fight. That stuff takes time. I mean, I can spend 10 minutes searching a room in my house for something I know is there.