In OD&D, every weapon did 1d6 damage, at least until people started house-ruling it away (I think in Supplement I, but certainly in AD&D and post-Holmes.) Over on another blog, Coopdevil has come out squarely in favor of every weapon does the same damage. He even defends it against objections about two-handed weapons.
Even though I've dabbled in converting The Fantasy Trip's approach to weapons to D&D, I'm very strongly pro-d6 only. I see it as inextricably tied to the "hit points are luck" viewpoint. If hit points represent a character's ability to outlast an opponent, and if they increase as the character gains levels, then it makes no sense for a sword to do more damage to hit points than a dagger. Of course, if you're using 1d6 for all weapon damage, then you should really be using the d6 as the base hit die as well... but that may be a topic for another post.
I have been fiddling around with ways to make different weapons feel different while still keeping the "every weapon does the same damage" rule. Perhaps this topic explosion on the blogosphere signals a good time to start talking about it.