Almost all components and peripherals have ESD protection built into them, designed specifically to prevent human contact causing issues. There should be no reason to be worried about damaging your peripherals (or, especially, your PC). Are you having issues with components dying randomly or something?
Before I started taking mitigation steps [0] yes. Sometimes my monitors or keyboards would shut off or get frozen and wouldn't work until I power cycled them. I broke my Ethernet port once when I blindly stuck a USB cable into the Ethernet port and gave it a big zap. I had a lot of other gremlins which I can't conclusively blame on ESD but I eliminated other possible causes. ESD protection isn't perfect and degrades every time it's used. I was giving multiple painful shocks per day.
