Fun old thread here. I double-checked to make sure I hadn't already posted, and my new build is so close to being done that I'm going to count it: Five!
1964 Armstrong 3-speed
1987 Diamondback Ascent (drop-bar, fixed-gear conversion)
1987 Bianchi Sport SX (the new rando build)
1988 Bianchi Premio
1991 Bianchi Eros (my first road bike!)