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
I was told that 제발 is a sort of kdrama phrase that isn't normally used for "thanks" in everyday speech. If this is the case, it might be a good idea to add a note
제발 is more so used in a begging manner than in a polite manner. 주세요 Would be used if asking for something politely.