Can drinking too much water be bad for you?

Yes, drinking too much water can be toxic - except it is very hard to drink too much fresh, clean water to be able to die. Normal healthy people would need to drink on the order of 20 liters per day for it to be toxic but people with some medical problems, particularly the elderly and very young, can get toxic on much lesser amounts. Also people with psychiatric disorders, most notably schizophrenia.

Drinking too much water is called polydipsia. This, as well as several other processes, can cause low blood concentrations of sodium, which is known as (dilutional) hyponatremia.