Generally, IMC, the monsters run when the morale rules say that they do. That means that sometimes run when they (logically) should've fought and fight when they (rationally) should've run. It also means that the boring tag-end of fights where the winner is already obvious seldom have to be played out.
I've tried to set up a precedent where some enemies might give up good intel after surrendering. The party has thus accepted surrenders, but have not tried to tactically force enemies to surrender (they might ask them to via threat, but not block off exits, etc.). If it's important for one reason or another, how the party handles a prisoner is also an okay way to gauge alignment or personality.
Side note: I have special provisions for XP and loot that provide incentives, or perhaps more accurately, drop the disincentives, for solving encounters in ways other than fighting. So if they talk their way out of an encounter, they get XP for it, and karma loot later, same result as if they had just killed everyone. I don't do this for runners, though. If the runner is significant enough, they'll track it down, or it's a recurring enemy or something.
As for chasing down runners, if an enemy runs while combat is still in full-swing, it's pretty much assumed that runner just got away, unless the players tell me they want to track it down, but it's a tracking situation, not a following situation.
In the 3.X campaign that I ran for about three years, I initially made the party's opponents attempt to flee when the combat began to turn against them. The problem that I encountered was that the rules make it really hard for most combatants to flee, and so most of the retreating foes wound up with a back full of arrows or chased down and AoO-locked by the more mobile members of the party.
This left me with a problem: Making sure that your opponent doesn't get away is practical from a tactical point of view, but shooting a man in the back or cutting him down as he attempts to flee wasn't feeling very heroic or exciting to my players. It's like machine-gunning the lifeboats after you sink an enemy's ship; only a raging man-bone would brag about doing something like that.
So these days my villains only run if they have a reasonable expectation that they'll get away (and in a game that features both magic and ranged superiority, that's not an expectation that they have very often). They're living in a world where very often the only way out is through, and they respond accordingly.
My bad guys try to run appropriately often.
Very intelligent, non-fanatical enemies will usually be the first to recognize an untenable situation and try to extricate themselves from it. Unfortunately for the PCs, these enemies are usually also the ones most likely to have an actual strategy for escape, so they often succeed...
Pretty much agree with Jeffs list.
Some will fight on, but there's a lot of reasons (and occasions) when the bad guys will leg it.
Unless they're mindless, my monsters don't stick around when they're close to death.
This hasn't always worked for them. Last session, I had a dread ghoul "run" away down an 80 ft deep well (they have a climb speed of 20 ft), and the alchemist dropped bombs down the well before he could reach the bottom and get out of the way. (The other dread ghoul fought to the death, but mostly because he didn't see an escape strategy.)
In another session I had a regular ghoul run away. Run Run Run away (at 4x speed, in a straight line) and he ended just inside the range for the party sorcerer's magic missile so he didn't escape either, but he was the second of two trying that technique. The first got away because the sorcerer was paralyzed when he fled.
I had a vampire-festrog try to flee when flanked once. He had a weaker party member between him and his escape route, so he spent a full round action dropping that party member unconscious with a full attack (bite, claw, claw). Then another party member took up that party member's position over the fallen party member, so he had to spend another full round attack action to drop that party member unconscious, and he was finally able to flee on the third round. (He had full HP+5 temporary hitpoints when he fled, but he hadn't even been trying to fight the party.)
Almost never, unless I especially want to emphasize the creatures are being cowardly. Sometimes they'll withdraw in order to call for help, or draw the players into an ambush, but otherwise fights are generally to the death unless the players decide to hold back. I don't believe that's ever happened.
Running this game, realism is pretty far from my list of concerns, so I assume that anything that's willing to attack the obviously armed and dangerous party must not love life or have much sense to start with.