What I've heard is more of a range than a set amount. Quite a few people have said that you should get between 20% and 30% of your calories from fat, so of course how many grams would depend on how many calories you eat per day. The sources I've read disagree on how harmful it can be to go TOO low, but that's not a problem for most people who eat well-balanced diets.
Others may have more specific input for you, though.
Good luck!