I've got a 68 Bassman head.
I've had it modified a bit, mostly on the bass channel and in the power section, to get it sounding the best for what I do. I can get a great clean tone out of it and some awesome overdrive cranked up, but it's not a very versatile amp on its own. The beauty of this amp is how responsive it is to pedals. Hit it with a nice Marshall in a box type pedal, it crunches and grinds like a Marshall. Hit it with a tube screamer and it will get you classic blues-rock tones a la SRV. Hit it with a nice fuzz (especially muff based fuzzes) and it roars like a far more powerful amp (Sunn or something).
Modulations can sound wonderful with a bit of thought. Since Bassmans in general are usually not breaking up much on their own, it helps to think of your drive section as your preamp, and anything after it as your effects loop, the last pedal in line being the in to your power amp, per se. I have great success running a tremolo, phaser, delay, and reverb into my Bassman that way.
They're great amps if you can use them at at least good gigging volumes. Down at apartment/quiet home levels, they'll sound like pedals into a quiet amp, just like anything else.