Staircases

Staircases connect the different dungeon levels to each other, but there are other means of connecting levels: ladders and portals. While ladders mean no difference in use, portals are a magical conection and may be unusable.
Usually, there are two staircases per level: one upstairs, and one downstairs. Each staircase is accessible in both directions, except the one leading from the Valley of the Dead to the Castle level: there's no downstairs on the castle level, so don't accidentally block all the trapdoors!
On branching levels, there are additional staircases. These are the entrance level to the Gnomish Mines and to Sokoban with one additional staircase. In Gehennom, there are the levels containing the Wizard's Tower which have one or two additional ladders (I'm not quite sure about the correct names for the "real" and "fake" wizard tower, please correct me here!).
The bottom levels of the Gnomish Mines, Gehennom ant the Quest as well as the top level of Sokoban only contain one staircase, obviously.
One other staircase is very important, and that's the upstairs from level 1. If you don't possess the Amulet of Yendor and climb up these stairs, you escape from the dungeon and lose the game. If you carry the Amulet, you reach the Elemental Plains and start the Endgame. In both cases, you can't return, and you are warned with the message "Beware! There will be no return!"