When I explore mineshafts (and caves) I do so at a blazing rate - I run down the corridors lighting them up and killing mobs and clearing cave spider spawners until I reach a dead end or complex intersection, then backtrack and mine ores and rails and loot chests, exploring side passages along the way back; I've never used any sort of navigation despite all of this, which IMO contributes to how quickly I can explore them; I've explored as many as three separate mineshafts (three dirt rooms, which mark their starting point) in one day, taking perhaps an hour to explore an average mineshaft, and have explored over 200 in one world (a guess, since as previously mentioned they are less common closer to the origin, plus I modded my otherwise vanilla world so they don't generate in areas with high cave density, reducing them by about a third - which is still about 66% more common than they are in 1.7+. This modification was done relatively recently though; a large area was explored with the maximum 1.6.4 mineshaft frequency of one every 100 chunks (150 after reduction, 250 in 1.7+), which is also about how much I explore per play session so I can still expect to find one almost every play session).
Note that I do carry around a map (fully zoomed, so not very precise) but that doesn't really count as navigation; it is mainly to show where I have been in general. I also leave markers (cobblestone and torch pillars, as outlined on this image) where I left off when returning back to my base to empty my inventory and get more food and wood, and occasionally after I've found a new cave or mineshaft and don't plan on exploring it right then, but those don't really count either.
For an idea of how quickly I explore underground, here is a sequence of renderings made after four consecutive play sessions, plus a zoomed-out map of the same area after two more play sessions (the area shown in the first set of renderings is to the lower-right - and even the larger map is only a fraction of my world; you can see part of a railway I recently made for the express purpose of quickly traveling back to my main base over 1,600 blocks away from my southernmost exploration point - there appears to be a VERY large (by 1.6.4 standards, which is much larger than 1.7+) cave system around 0, 1900 (seed -123775873255737467); you can see multiple exposed lava pools in the cave system near the bottom, which will all be obsidian-ified when I'm done exploring it):
I also don't miss much while exploring at this rate; here are some screenshots of some areas I explored taken in MCEdit (aka "poor man's spectator mode", since that is only in 1.8+):
Under my main base; this is the only area with mine tunnels dug at y=11 (I actually branch-mine to get resources early on, plus in this world I did not start caving like I do now for a month or two):
This is an example of a large cave system in 1.6.4; a solid mass of caves with a 100% chance of hitting one if you try mining through it, either vertically or horizontally:
Most of what I "miss" is just stuff like this, with no connection to the surface or any other caves (you can see some mineshaft corridors I missed near the left of center):
When I explore mineshafts (and caves) I do so at a blazing rate - I run down the corridors lighting them up and killing mobs and clearing cave spider spawners until I reach a dead end or complex intersection, then backtrack and mine ores and rails and loot chests, exploring side passages along the way back; I've never used any sort of navigation despite all of this, which IMO contributes to how quickly I can explore them; I've explored as many as three separate mineshafts (three dirt rooms, which mark their starting point) in one day, taking perhaps an hour to explore an average mineshaft, and have explored over 200 in one world (a guess, since as previously mentioned they are less common closer to the origin, plus I modded my otherwise vanilla world so they don't generate in areas with high cave density, reducing them by about a third - which is still about 66% more common than they are in 1.7+. This modification was done relatively recently though; a large area was explored with the maximum 1.6.4 mineshaft frequency of one every 100 chunks (150 after reduction, 250 in 1.7+), which is also about how much I explore per play session so I can still expect to find one almost every play session).
Note that I do carry around a map (fully zoomed, so not very precise) but that doesn't really count as navigation; it is mainly to show where I have been in general. I also leave markers (cobblestone and torch pillars, as outlined on this image) where I left off when returning back to my base to empty my inventory and get more food and wood, and occasionally after I've found a new cave or mineshaft and don't plan on exploring it right then, but those don't really count either.
For an idea of how quickly I explore underground, here is a sequence of renderings made after four consecutive play sessions, plus a zoomed-out map of the same area after two more play sessions (the area shown in the first set of renderings is to the lower-right - and even the larger map is only a fraction of my world; you can see part of a railway I recently made for the express purpose of quickly traveling back to my main base over 1,600 blocks away from my southernmost exploration point - there appears to be a VERY large (by 1.6.4 standards, which is much larger than 1.7+) cave system around 0, 1900 (seed -123775873255737467); you can see multiple exposed lava pools in the cave system near the bottom, which will all be obsidian-ified when I'm done exploring it):
I also don't miss much while exploring at this rate; here are some screenshots of some areas I explored taken in MCEdit (aka "poor man's spectator mode", since that is only in 1.8+):
This is an example of a large cave system in 1.6.4; a solid mass of caves with a 100% chance of hitting one if you try mining through it, either vertically or horizontally:
Most of what I "miss" is just stuff like this, with no connection to the surface or any other caves (you can see some mineshaft corridors I missed near the left of center):
TheMasterCaver's First World - possibly the most caved-out world in Minecraft history - includes world download.
TheMasterCaver's World - my own version of Minecraft largely based on my views of how the game should have evolved since 1.6.4.
Why do I still play in 1.6.4?