I've got a friend with a Tilley. He loves it. Swears by it.
But for me, it's a Filson:
That's Filson's tin-cloth "Bush" model; I've also got a white, light-weight Filson "Packer" hat for summer; it's more floppy because it uses shelter-cloth, and it's also got a smaller brim.
White's better around ticks, by the way.
Filson still makes their original hat, too, which is an outdoor version of the pork-pie.
Tilleys are great. But I'm surprised no one else had mentioned Filson until now. A Filson is as durable as a Tilley, but I think it's a little more basic in execution. (I'll bet if this were a fly-fishing forum, a ton of posters would have mentioned Filson. But I'll confess I have no stories to relate involving elephants. . . .)
Anyway, I have the same affiliation with Filson that Mickey has with Tilley. We don't get any pay; we just love our respective hats!