When I work inside my computer to replace RAM, should I unplug it or leave it plugged in?

I've found conflicting opinions about this. Some say leave it plugged in so it will be grounded. Others say unplug it for safety.

Does a wrist strap satisfy the grounding requirement?

Unplug it.

Wrist strap should be fine.

Sorry I read that wrong.

Odin is right

You can leave the unit plugged in. just don't have it on while you're doing this. Changing RAM however is one of the few instances in which I would do this. If you are working on just about anything else, like swapping a hard drive, or touching the CPU, you should unplug the unit

The safest bet is to unplug the unit. PC off still has small power for led lights and some info can be saved in memory. If the PC is off you would be OK, but if there were open folders say saved in memory for when you restart, they would be gone. I have never owned a wrist strap but I do touch the metal of the case to discharge any static before I play.