Maps and what they where...

[Griogre]

YMMV = Your Mileage May Vary. Or my way may not be the same as your way.

[Tokuriku]

In fifteen years, I've never had players map out a dungeon as we played. Online or offline. The most I do is map out an area for an encounter on the battlemap or provide a handout for local areas.

Well, I can definetly recommend the technique.
It is one of those things you have to try to understand it's value.
In my experience with roleplaying games (whatever game it might be) mapping has been an intresic aspect of the game.
It is one of the facets of roleplaying just like receiving xp at the end of a session or for acomplishing something great is.
If you take it out, then I believe your at some loss.

Let me give you a nice analogy.

One GM I know does not give xp. When he thinks you are ready to go up a level, he gives it to you. This is fair in my opinion and for most cases more then valid. First he doesn't have to give you the reasons why someone levels faster then another. Second he eliminates discriminatory xp givings like xp for monsters based on the damage you did to it (the way it worked before) where fighters would level faster then wizards for exemple.

The negative aspect is... well... most players strive for xp be it in the form of roleplaying well or from combat. When you see xp ranking in, you see that your character evolves and it is appealing. Take that away from players and it's the same as taking mapping away from the characters.

One thing I can say specifically about player mapping is that when a player takes time to draw a room by him/herself, the room and it's dimensions get ingraved in that person's mind. They have less of a difficulty understanding the limits of their environment and what is possible or not in that space. I usually have players who are very inventive and don't bug myself to only the maneuvers that are in the rules. Sometimes what they want to do is simply impossible. When they draw the paces themselves, it happens less frequently that they try for these impossible things wich basically mean that we are on the same page, we see the same thing in the minds' eye.