One obvious point is, try to walk in the middle of the path so you have some time to see any new mobs crawling up from the sides.Be aware of already cleared open or circular areas, so you know where to retreat and kite the mobs (well, what little kiting you can do in caves).
Are you playing alone or in a group? If alone, then do you take a follower with you? Both of these are factors in how to play.
In a group: Stay back and let the other team mates do the exploring, esp. any tanks like barb or monk (or any ranged who want to run ahead, they can take risks instead ;) ). You should still be within sight of the frontrunners, so that if some late spawns try to catch you they can quickly turn around to help.
Alone: Clear an area. Run ahead being very careful of any boss or elite mobs (don't get their attention), and then run back to the cleared area to AoE kill all the normal enemies that are chasing you. Warning: Unless you have really good dps this may not work well in Inferno.
With follower: Move slowly as your follower likes to attract elite mobs when you're trying to avoid them. Be aware of choke points if you're using Templar, as he can be a convenient human shield while you nuke from behind (though caverns paths are usually too big to block the little spiders :( )