So, I was talking to a friend about an issue in my D&D 4th edition campaign that generalizes to most (though not all) game systems. Specifically, it's incredibly difficult to escape a combat unless the fleeing character(s) have a movement mode not available to the pursuers. Xorn movement (a.k.a.earth glide) is the one I've seen in games lately, and that one is frustrating because there's typically nothing you can do to pursue at all, because who the hell prepares move earth? (Tangent: If you didn't read and memorize the description of xorn's earth glide power, the text of move earth goes out of its way to convince you not to use it. Read the last line of the spell description, just above Material Component. This makes me irrationally annoyed with the 3.5e writers; technically, the statements can be parsed so that they do not conflict, but the text of move earth reads as if it is warning you not to bother with this spell.)
But I digress. The problem is that Speed is a fixed value that a character can increase only by fixed amounts, so that (assuming you knew the stats) you could know with near-perfect reliability whether or not escape is possible (ignoring for a moment the matter of the pursuer not caring enough to pursue). I'm sure a lot of DMs are okay with this; the community of game-bloggers being what it is, I'm sure there are DMs who think that the intention to change the viability of fleeing is heresy of thought, heresy of word, etc. This is for everyone else. I've roughed out a version for 3.5 and 4th edition D&D. This is just an idea I had, and has received no testing whatsoever.
D&D 3.5: The Rout Action, version 1 (simple)
As a full-round action, a character may accept the panicked condition for 10 rounds (with the specific exception that the character does not have to flee along a random route). In exchange, the character gains a bonus to Speed equal to (1d6 x 5 ft) when moving away from all enemies, and then performs the Run action.
Randomizing the bonus Speed is important because predictability is antithetical to the suspense of a chase.
Simulationists will hate this; a Speed of 30 ft already implies nigh-Olympic level running speed, and the best possible roll doubles this Speed. You could apply the bonus as additional movement from the Run, Withdraw, or Double Move actions (so that it isn't multiplied by those actions), though that certainly diminishes its usefulness. (It also changes the action away from being a full-round action, and is more a kind of meta-action.)
This rule doesn't generalize in form to a footrace or giving pursuit, which is kind of unfortunate but outside its intended scope.
Thanks to boots of striding and springing, monks in general, and the overall range of monster speeds, it's entirely possible for the pursuer to be so fast that the speed bonus granted here is trivial, but at that point it's a matter of class or treasure resources, so... fine, whatever.
Since there's no comparable bonus for pursuers, it clearly favors the possibility of an escaping character successfully escaping, which I regard as by design; remind your players, if you must, that the escapee has dropped everything in his hands (see the panicked condition) and they still get XP for the encounter. Any attacks launched against the fleeing character have the clear benefit of the target being denied a Dex bonus to AC (as per the Run action).
D&D 3.5: The Rout Action, version 2 (more complex)
As a free action, a character may accept the panicked condition for 10 rounds (with the same exception, as above). When performing the Run, Withdraw, or Double Move actions and going away from all visible enemies, the character makes a Strength or Dexterity check (whichever is higher) each round to pour on speed, and moves an additional 5 feet per 5 points of success on the check. As the panicked condition inflicts a penalty to all ability checks, it is possible for a low-Strength character to gain no bonus movement.
It would also be feasible to have a Flee In Good Order sort of action, in which you accept the shaken or frightened condition for the same duration, but your Strength or Dexterity check yields 5 feet of movement per 10 points of success.
D&D 4e: A few notes on adaptation
In 4e, it is a good practice to resolve chase scenes with a Skill Challenge, and what I'm doing here isn't intended to replace that in any regard. The problem that I see is that it is at present a matter of fiat to shift from combat rounds and grid-based pursuit over to skill challenge mode, where your Speed stat (whatever it might be) avails you not, and many spellcasting classes can pretty much forget about it, as compared to grid-based pursuit, where the caster's long-range spells are superior to melee attacks.
D&D 4e doesn't have the panicked condition as such, so I'm adding it for my purposes here.
Panicked: Fleeing in terror. You grant combat advantage to enemies making melee or close attacks against you. You get a +2 bonus to AC and Reflex against ranged or area attacks from nonadjacent enemies. You take a -2 penalty on attack rolls.
D&D 4e: The Rout Action, version 1 (simple)
As a free action, a character may accept the panicked condition until the end of the encounter. In exchange, the character gains a bonus to movement when moving away from all visible enemies and making the Run action or taking a double move. This bonus is 1d6 squares at Heroic, 2d6 squares at Paragon, and 3d6 squares at Epic.
D&D 4e: The Rout Action, version 2 (more complex)
As above, but instead of gaining 1d6 or more squares, the character makes an Athletics or Endurance check to pour on speed. Depending on the environment or terrain, Acrobatics, Dungeoneering, Nature, or Streetwise might also be options, at the DM's discretion. For every 5 points of success on the roll, move 1 additional square when making the Run action or taking a double move away from all visible enemies.
4e Version 1 and Version 2 are really quite different in the top-end outcome, but I haven't played around in epic tier yet to see if potentially as much as 18 extra squares of movement is good or bad, or really even what a character's skill bonuses are likely to be at that level. If you wanted to use version 2 for footrace rules, it would be entirely within reason to treat the panicked condition as representing sprinting.