Mark Engblom did a terrific series back in 2008 on Superman's Fortress of Solitude, concluding with a look at 12 different Fortresses he'd had (in comics and in film), including two that didn't belong to Superman. One belonged to Bizarro, and the other to Krypto. I found a few months later that Supergirl briefly had her own Fortress, but she destroyed it after it was accidentally discovered by an unscrupulous archaeologist.
Here are two more that I've come across recently. Superboy's "Secret Cache 3" is somewhat similar to the Outer Space Fortress over there, but note that that's described as being disguised as a meteor, while this is inside a crater on a barren world:
In World's Finest #156, Bizarro visits Earth and creates the Fortress of Crowds as an answer to Superman:
Update: I should have given Blog Into Mystery a hat-tip on the Secret Cache 3 part of the post; while reading his blog, I noticed a post about the cover to Superboy #109 which encouraged me to read the issue.