In zoology, a sessile animal is one that cannot move from one place to another; those that can are referred to as motile.
Only seven monsters are truly sessile in NetHack, although there are a larger number with relatively slow speeds. The sessile monsters are:
Truly sessile monsters can normally be left alone; even if they block a corridor, the player can usually dig around them or teleport them away safely. This contrasts with slower-moving monsters, such as floating eyes, which can move and block players if left unmolested.
Killing high-level sessile monsters while avoiding their passive attack can be frustrating; there is no way to retrieve any missiles thrown at them until they are killed, short of teleportation or taming; slow-moving monsters move eventually, allowing missiles to be retrieved. Players should therefore use rocks and other junk to kill such monsters.
Sessile monsters can be used by players to block all monster access to certain squares, to cover a stash or to protect a boulder fort from giants, for example. Typically these will be generated by reverse genocide. The player may wish to tame the sessile monsters to be able to move them around, although this means that magic whistles should not be used on that level. Many spoilers propose blue jellies for this function: unlike the molds, they are unlikely to be killed in a single blow by a careless player, and unlike spotted jellies, their passive attack is easy to gain resistance to. For a careful player, however, any sessile monster will do.
Polymorphing oneself into a sessile monster normally leads to one of two outcomes very quickly, from the player's perspective -- either the time on the polymorph expires, returning the player to his or her previous form, or a hostile monster attacks and kills the player, returning him or her to the previous form. The player will not get an opportunity to move while sessile. However, a source of speed will allow the player to take the occasional turn (although still not to move).