Original band members

Dungeon would almost be in Megadeth territory. :)

Only one I can think of that stayed pretty constant for a long career was Crowded House, it just depends on whether the other Finn brother with the tambourine counted as a member or not.
 
Well obviously they have a different drummer now since Paul Hesters death. Tim Finn was an official member even though it was only temporary. They did have another member but he left before they actually recorded anything so he doesn't count.

Apparently Satriani did backing vocals on the first LP.
 
Crowded House's line-up changed a fair bit, actually. Tim Finn joined and then left again, Mark Hart came into the line-up and then Hester left and Peter Jones filled in for a while until they did their farewell show. Obviously, it was fairly stable compared to a lot of bands, though.
 
Serpent (UK) - 1976 to present without a line-up change, although they are on enforced 'sabbatical' since Rob Python was jailed for consorting with a donkey...
 
That's because they were underappreciated, so underappreciated (why is underappreciated coming up with a red line underneath - isn't it a real word?) that very few people have heard of them. Most of the other bands stole their thunder - that, and turmoil within the group, pretty much held them back.

Way of the Serpent, The Serpent Rises, Rise of the Serpent... great stuff.