My favourite is from when I was in grad school and I connected two network interfaces from the same subnet onto a virtual bridge. This effectively meant my box was repeating all traffic on our lab's subnet. I was trying to debug my own network problems and was puzzled why I was getting duplicate ping replies. I left for class and figured I'd debug it later. Halfway to my class I finally clued into my mistake and rushed back to the lab. One of my labmates asked me if I was having Internet problems. I secretly reached under my desk to pull one of the two network cables and said no and we all got on with our day :)
Luckily, our DBAs were quick to restore it. This was in 2001 and doing postmortems wasn't common back then.
Was trying to delete files in a folder but had root access to a prod server in another window. Wiped out a server that was supporting around 20 traders.
Went to the backup tapes and restored that server from a previous day's backup.
No one ever noticed.