17,321,603 eligible voters

And here's the breakdown. I'll list some of the bigger numbers:
Taipei City: 2,042,805
Kaohsiung City 1,163,446
Taipei County: 2,878,477
Kaohsiung County: 953,610
Taichung County: 1,135,237

Edit: N.J. noticed the Taipei area has roughly 25% of eligable voters and asked how turnout compares across regions.

In 2004, turnout across the country was very near 81% in all major -- 81.41% in Taichung, 81.31% in Taipei County, 81.15% in Tainan County, and 81.56% in Kaohsiung County, 81.71% in Taipei City and 81.81% in Kaohsiung City. So no real differences there. In 2000, turnout was between 83% and 85% in most places.

Turnout was significantly lower in both elections in the outlying islands, Hualien and Taitung, averaging close to 70% in 2000 and 67% or so in 2004.