Carseat Bases.. Do you have to use one?

tstaggs2012

I don't mean to sound like I'm going to put my LO in danger.. I'm installing the car seat base that came with the set in my car and I told BF we would have to find an extra base for his car/grandparents etc.. He asked if you have to always use a base... I wasn't sure because I have seen some that just strapped the seat in safely.. I have the Comfy Carry Elite by Safety First and was just wondering if I could do that or if I need to find another base?