How can I escape from monsters quickly in Minecraft?

I am usually able to escape monsters quickly and easily by carrying boats with me, and staying close to the shore whenever possible. This allows me to make a quick getaway from monsters whenever they get close, since the boats let me travel much faster than running or walking, and consume no hunger either. Boats also can move much faster than any hostile mob, which makes it easy to outrun them.

You could also just start digging. Dig 3 blocks down in a stairway formation real quick, and then start tunneling home. Be sure to throw a few blocks behind you to prevent yourself from being followed.

I find that the most effective way to escape is to simply build a small 1x1x2 hut around me, tab out, and wait until morning. I generally carry a stack of cobble/dirt around with me, both for this purpose and for impromptu staircases.