In reply to Rich L:
Sadly, I lost my 13-yr-old T5 at Venice airport recently (probably put down when very tired and bored waiting for a delayed flight). They don't seem to do the cotton version in the same colour any more (stone), so I ended up getting a nylon one instead. Which, of its first test, seemed a fair bit cooler than the cotton duck version.
I preferred the T5 over the T3, due to the smaller, stiffer brim.
They're well made (my only gripe is that the sizing seems a bit variable these days; definitely try them on in a shop before you buy, and don't assume another one 'the same size' will fit; my recent experience). On the other hand, I saw some T3 clones on a market stall in Wareham a couple of days after I'd bought the new T5, and they looked pretty well made, too. If they'd had a T5 clone, I might have been a bit annoyed. I think they were selling for £8. The new T5 cost me £60, although I've seen them online for £55.
They have a reputation for making you look a bit of a prat ('silly Tilleys'), and are popular with ramblers and the mature mature person, but, oddly enough, I saw a young lad on a BMX bike wearing one the other day...