Well, if you do enough nonlethal damage that they won't recover before succumbing to thirst....
"A character can go without water for 1 day plus a number of hours equal to his Constitution score. After this time, the character must make a Constitution check each hour (DC 10, +1 for each previous check) or take 1d6 points of nonlethal damage."
So for a human commoner-1, that's 34 hours before making checks; after 11 more hours, the human commoner-1 can't make checks; after three hours more, the human commoner-1 will have more nonlethal damage than HP, and can't get up without someone else's intervention. So with 48 hours of forced thirst, a human commoner-1 can't do anything at all, ever, without help (if you use the ruling from the 3.0 FAQ that nonlethal damage from such things as starvation turns into lethal after a certain point, this means the commoner quickly dies after that, in just a few hours).
Nonlethal damage heals naturally at a rate of 1 hp per HD per hour; so that human commoner-1 will recover nonlethal damage at a rate of 1 hp/hour. Deal enough nonlethal damage to the human commoner that it won't recover enough to wake up at any point in it's maximum no-water time, and it's a kill, without intervention. So, for a human commoner-1, that's basically 50 points of nonlethal damage.
For the dwarven fighter 10 with 20 Con, on the other hand, he can go 44 hours without making checks, and potentially pass his checks until 16 hours after that (60 hour mark), and thereafter, if he always rolls minimum damage, it takes however many hours as he has HP before he's down for good.
As that dwarven fighter 10 will recover 10 hp/hour, you need to deal enough nonlethal damage that he won't recover in that time frame. Assuming the dwarf has the dice on his side as much as possible. 600 points of nonlethal damage for before he makes checks, plus 10 times his HP in nonlethal damage for all the 1's he's expected to roll, and he passes the point of no return, with 0 chance of recovering on his own.
Creatures with fast healing or regeneration have the same issues, only more so. The Big-T recovers 40 nonlethal damage per round, with an additional 48 per hour. As there are 10 rounds to a minute, and 60 minutes to an hour, that's 600 rounds * 40 nonlethal/round + 48 per hour, or 24,048 nonlethal damage recovered per hour. He has a Con score of 35, and so goes 59 hours before making checks. With a Con bonus of +12, it can make it's roll until it hits DC 33 after 24 more hourse (83 hour mark), and thereafter takes at least one point of nonlethal damage from thirst per hour until it runs out of HP (858 more hours, for a grand total of 941 hours), at which point it's at it's own point of no return, with 0 chance of recovering on it's own. 941 hours times 24,048 nonleathal damage/hour is 22,629,168 points of nonlethal damage to make Big T not come back without aid (assuming you can lure him somewhere where water won't dribble into his mouth or something....).