Nothing that useful.
At the county hospital our call room was setup as several bedrooms spilling into a common living area where residents hung out playing video games, watching TV or charting. One of the doorways into the living space had a pullup bar hanging from it. Residents so inclined did as many as they could and wrote their name, number of pullups and witness. There was a never ending contest to see who could do the most.
The plastics and ortho residents had a inter-departmental yearly contest at a local park called the Skin and Bones Games that was eventually opened to all surgical residents. It was comprised of conventional things like number of pushups in 1 minute, 100 yd dash and a kickball game as well some more unconventional stuff like hotdog eating contest, donut relay (eat a bunch of donuts and then run a 400 as a team of 4 in relay fashion), egg toss, wrestling in padded sumo outfits, mechanical bull riding and some others that I can't seem to remember.
We also had a residents vs faculty softball game which provided a nice opportunity to beat up on faculty.
We did have open and lap skills stuff that we did in the simulation lab. Times may have been posted but they were never celebrated or resulted in the banter that followed the stuff above.