제발 is more of an intensifier than what we would think of as 'please.' In most situations, the polite verb ending performs the function of the English 'please' (e.g. if you want some water, say "물 좀 주세요,' NOT "물 좀 제발"). If you're begging for something, then 제발 would be appropriate (for example, my students would often say "Teacher, 제발!" when they wanted to get off homework.
Source: my Korean tutor + teaching experience