Zombies obviously can't, but skeletons and ghouls can run (×4 move) right?
But for how long? Can they run for days? Weeks?
Can incorporeal undead like wraiths, shadows and ghosts run?
Do they suffer any damage like living creatures suffer non-lethal (immune?) for hustling for hours (and mounts suffer lethal)?
Can undead armies just run around at 12 times the speed of normal armies (with no baggage train too)?
Creatures of the type undead typically have Constitution as a nonability; the Monster Manual on Nonabilities says, "A creature with no Constitution cannot tire and thus can run indefinitely without tiring (unless the creature’s description says it cannot run)" (312). Undead creatures (including incorporeal undead creatures) can take the run action even while flying: "A creature can use the run action while flying, provided it flies in a straight line" (MM 312). Undead creatures are also immune to nonlethal damage, so such creatures can hustle forever without issue.
This DM wouldn't allow such massive speeds for undead ground forces. In my campaigns, difficult terrain and obstacles are fairly frequent in most wildernesses, and both impede the run action, which requires the creature travel unimpeded in an unobstructed straight line. While the ability to travel without rest essentially doubles (or possibly even trebles) an undead ground army's overland movement, I can't imagine the ability to flat-out run tirelessly being strategically valuable even in the most desolate of campaign settings; a wilderness will have bad footing and stuff in the way. Seriously, even Athas has rocks.
There's the possibility, I guess, of scouting the terrain beforehand, clearing away obstacles or even building roads, but then the undead army's (ahem) dead run to its next engagement is slowed instead by all that preparation. It would take extraordinary circumstances for me to view the land-bound undead army's ability to run forever as a broad, easily leveraged advantage over a traditional army rather than an interesting quirk.
However, an airborne army composed of allips, shadows, spectres, and wraiths can certainly tirelessly run while flying, traveling quadruple (or eight times or twelve times) its (slowest members') fly speed! Such an army will rarely face difficult terrain or obstacles in the air, after all. But such an army of any significant size has a good chance of obliterating most campaign settings anyway, the airborne undead army's ability to run forever while flying being merely a footnote in the larger, sadder history of events. Faced with such an army, the end result's almost always the same: Just about everybody dies.
