My husband and I run them for ourselves and occasionally close friends, particularly when it's an online survival game like Rust, 7 Days to Die, or Ark: Survival Evolved. I despise playing online with random people because I'm interested in the survival/building/dealing with monsters aspect of the games, but everyone else just loves to be an *** and destroy everything you've worked for.
We've also run private servers for ourselves for stuff like Terraria and Minecraft, and a few years ago we played around with a private WoW server for shiggles. Have some hilarious screenshots from that.