My favorites were the Eliza clone, and ICBM, where you are trying to intercept an incoming ICBM with a anti-ballistic missle. My first use of trig functions, which really helped solidify the concepts to me. I also converted the 2-D version to 3-D (with altitude) for even more fun.
I was originally using a TRS-80 Color Computer, with a slightly different dialect of BASIC, so I was usually having to make modifications. Which also helped me learn programming.
Great, great times.