"Quiero que bebas más agua."
Translation:I want you to drink more water.
Regarding the "Quiero que (fill in the blank) mas agua" type of exercises: I'm just picking up on this now, so I may be wrong. Responses such as "bebe, bebemos, bebes, beben" are incorrect because they have an "e" in the conjugation instead of the "a." There's no ambiguity about informal you vs we, etc.
I want you to drink more water. In this English expression "I" is the subject of "want", but "you" is the one that is supposed "to drink". In Spanish, "Te quiero beber" is "I want to drink you." which is not done. They must say "I want that you drink more water." which is "Quiero que bebas más agua.". There are plenty of examples at this link: http://spanish.about.com/od/verbmoods/a/when_to_use_subjunctive.htm
Check out pezguy's comment above.
"Quiero que" requires that the following verb be in the subjunctive, because you are trying to influence someone else's behavior. The only subjunctive form available was "bebas."
Your sentence "I want to drink more water" does not need the subjunctive because you are not trying to influence anyone else's behavior. So it uses the infinitive (beber) instead of the subjunctive: Quiero beber más agua.
I want to study: Quiero estudiar. I want him to study: Quiero que él estudie.
I want to run: Quiero correr. I want them to run: Quiero que corran.