Well, I can think of two reasons that this might happen.
The first is if you didn't replace the headlights with 12v sealed beams, and you have bosch relays. I know, a lot of people tell you that you can still use them. The problem is that the 6 volt lights have a lower resistance, so they tend to suck a lot more current through them. And, the resistance drops when the filament heats up. As a filament's resistance drops, it starts drawing a dramatically higher amount of power. Bosch relays can "lock" in the on position when a lot of current is passed through them.
The second way it can happen is trying to mate a 6 volt positive ground system to a 12 volt negative ground system - with relays. Bosch relays can be triggered by either a 12 volt source or a ground. In your case, you might have mixed the two types of circuits by trying to keep the old headlight switch in the circuit. If wired wrong, this may have accidentally caused the circuit to fail in the ground position - and if it is hooked to the ground trigger side of the relay the lights will stay on after the fuse blows.
