When replacing fence post do I use cement

I didn't use cement, just prepared with a post hole digger and set in the post and filled in with dirt.

I would definitely recommend a concrete footing. You can do it using the "dry pack" method... dig the hole (best way is with squared corners), put the post into it and pour some pre-mixed concrete right out of the bag (dry) into the hole about half way up... pour in some water... mix it with a stick or shovel... pour more in... add more water... mix... etc.