Do I need Spanning Tree Protocol?

The purpose of spanning tree protocol is to allow redundant connections between switches to exist without creating loops that would bring the network down.

If you did not have those switches in a stack, then yes you would need stp, and you would be in no doubt about it, within seconds of you connecting the last link completing the loop (for the sake of discussion the cable between switch A & switch C), you would have had a non-functional network - non functional as in no traffic across the LAN - and all the active ports lights flashing furiously.

If you have stp enabled and you want to know if it's required, remove the A~C link (or any one of the interswitch links), and then disable stp on all switches and then reconnect the cable, the LAN will either stay up or go down - if it goes down, you need it, if it doesn't you don't - if you do, disconnect the link to break the loop and reconfigure.