How do I delete some of my old saved games?
Or can I?

Ordinary Civ III save files are stored in the Saves directory of your base Civ III directory. PTW Saves are in a Saves folder in the PTW folder, and Conquests Saves are in a Saves folder in the Conquests folder. Saved games have the extension .SAV . I imagine it is ok to simply delete these at will. There is also an Auto folder, which contains 6 or 7 autosaves from the last game you played.