Depends on what you are using, what you are keeping in (or out) and how much maintenance you want to do.

I fenced in a yard for my dogs with 4x4’s and packed driveway stone around them. 4 years in they haven’t budged, they are at MOST 3 feet deep probably closer to 2.5

Pounded cedar posts in for livestock, tend not to go as deep, but you may have to do some maintenance every year or so to pound a few back in or straighten some out.