The easiest way to do this is to use a scroll of teleportation or a teleportation charm. It will immediately get you far away from danger, but it may send you into a different bad situation.
A wand of teleportation will send a single monster far away.
Another way to do this is to use a staff of blinking. It will send you a few squares away from the monster, allowing for a ranged potion or staff attack or some other escape method.
Jumping down a nearby chasm can help you avoid immediate danger since monsters will not follow you. Drinking a potion of descent is similar, but nearby monsters will fall down with you. Nevertheless, you'll take fall damage and may fall into another dangerous situation.
Drinking a potion of levitation can free you from eels, bog monsters and krakens. You can attack them with impunity while levitating.
A scroll of sanctuary will block monsters from entering melee range of you in the cardinal directions (up, down, left, right). The monsters can still melee you diagonally, so positioning the sanctuary runes is important. Also flying monsters ignore the sanctuary runes.
If you're caught in a net, you can set the net on fire with incendiary darts or a staff of firebolt. This will set you on fire, but you'll be able to move freely.
Throwing down a potion of confusion can cause nearby monsters to accidentally attack each other, or at the very least not attack you most of the time. Similarly, reading a scroll of discord or casting a staff of discord will cause monsters to spend precious turns attacking each other instead of you (although the remaining discordant monster will still attack you in the end).
A wand of polymorphism can transform a very dangerous monster into a much less dangerous monster (or just into a different dangerous monster). But if you're already about to die, then your odds are usually better with door #2.
Drinking a potion of invisibility and just walking around a corner sometimes resets the monsters back to wandering. But it works best before the monsters are already on top of you.
Or you can just quit the game and start again if you have no options and don't want to see your character die.