How many recommendation letters should you ask a professor to write? Say a student who wants to further her study in a specific field, so she applies for multiple programs at several universities. Each of these prospective universities requires her to submit at least two recommendation letters. The question is that how many recommendation letters should she ask a Professor to write? 
If she has applied for 5 programs at 5 universities, then she needs to submit 10 recommendation letters. She knows 10 professors of her former school, in this case, should she ask each professor to write one recommendation letter for her, or ask the two professors she knows best to write 10 recommendation letters for her?
Normally, you should choose the two people who know you best and can write you the strongest letters, and ask each of them to send one letter to each program to which you are applying. Each of them will write one letter and send copies of it, with minor modifications if needed, to every program, so it isn't much more work than sending one letter.

This is to your advantage (you get the strongest letters) and also minimizes the total amount of work.

If a program needs more than two letters, or you think another professor would be a more suitable writer for one particular program (for instance,  if they have connections to that institution), then you can ask for letters from them as well. But there's no need to get letters from more different people purely for the variety.