Enemies do not necessarily have to be killed, although doing so tends to get them out of the way for the rest of the game. Monster behavior, Rotting Meat, hiding spots, and Flares can be used to avoid combat, though any enemies spared will need to be avoided any time you want to pass through an area.
The following is a list of ways to bypass enemies. Stop reading if you want to figure it out for yourself :)
1. Monster Behavior - Most enemies pace back and forth, and only attack or notice you if you get close enough to them. Sometimes it's possible to just wait for the enemy to walk out of range of what you need. Rotten meat can be used to temporarily lure enemies further away, but will only allow you to run past them if you are hiding, or use a flare.
2. Hiding spots - While hiding, you cannot be noticed by enemies, or hurt by enemies that have already noticed you. It is possible to hide while an enemy is at one end, wait for it to move past you(or lure it there with rotting meat before hiding), then leave hiding and continue on.
3. Rotting Meat - You can use these to cause thin men to leave their standard pacing zone, rushing toward wherever you drop the meat, multiple thin men can be occupied by dropping multiple pieces. However, you cannot move past the monsters while they are distracted, so it has to be used in conjunction with hiding spots. If you leave the area and come back, the monsters will have moved back to their original position, but if not otherwise distracted, they will remain standing where the meat was dropped, and can be redirected with more meat.
4. Flares - You can use a flare to temporarily immobilize any enemy within a certain distance. The enemies will recover after a certain period of time, or immediately upon leaving and re-entering the area. Aside from hiding, this is the only way to simply run past an enemy. Since handgun bullets can be traded for flares at a 10:3 rate, this can actually be quite efficient if you only need to pass an area once or twice, since one flare costs the same as killing a thin man outright, and it is possible to affect more than one enemy at a time.
5. Relocation - There are certain areas that can be used to permanently occupy a thin man, so as to get it out of the way permanently without killing it. You can lure a thin man into an adjacent room, so long as there is no door blocking its path, and there is a hiding spot to allow you to escape afterward. Thin men moved in this way will remain in the new room indefinitely.
6. Ham - There is at least one situation in which you can sacrifice your most treasured ham in order to non-lethally and non-violently get a thin man out of your way permanently. This is the only way to bypass this particular thin man without violence, as you will not have flares yet.
7. Leg Shot - I'm going to give you guys the most useful hint in the game. There is a way of bypassing all thinmen much quicker than using meat. If you shoot the legs of a thinman, during the reeling animation you are able to pass freely through them. Obviously it's non-lethal so can be used to traverse areas quickly on a pacifist run. - Nick Byrne