Actually you "could" go broke if buying H-D specialized tools unless your need and skill level are up to the task. Follow the links Tank provided for the basics...and you will be on your way...the specialty tools should follow if you stick with it. :s
If you care to carry a small tool kit on your bike for short order "roadside assistance" you will want special set of Torx, Allen Hex Drive and 1/4" & 3/8" drive Phil and Slot driver sets of the fasteners you may need on the road. Zip Ties, fuses, pliers and plug/socket...small DMM are the basics for me.