In 99.99% of computers, you don't have to fill all the memory slots.
We can't know this for sure with your computer, as you didn't leave any information about your mystery computer.
With computers that use RIMMs, you either have to fill all the slots with RIMMs, or with Continuity RIMMs.
With PowerMac G5 towers and with the Macs that use FBDIMMs, you don't have to fill all the slots, but you have to populate in identical pairs of DIMMs.
The quick and easy answer is that if your computer boots up and runs the OS, you don't need more RAM, but more RAM can help it run faster.