My favorite lately is Tori Richard's "cotton lawn" (echoing Flanderian, from whom I learned about the brand in the first place.) Honestly, it's pretty tough to beat for summer comfort.
I also quite like Tori Richard's machine washable silk (I just don't buy shirts which need to be dry cleaned), though they only have a few models in stock currently.
Traditional fabrics, I like Madras (real Madras, not the kind of twill Brooks Brothers has passed off as Madras lately), and linen too. I'm okay with rumpledness.
If I can find it, I really like hemp. I have a Japanese jinbei in hemp, and it's really great in hot, muggy weather (like Japan in summer). Prana sometimes does a hemp shirt in the warmer seasons; probably any progressive-y yoga-esque brand will have some hemp apparel. Oh, Prana has some hemp trousers (using the word loosely) as well, which are great as home wear. A bit pajama-ish to actually wear out of the house, though. I'd love to have a hemp utility shirt in some kind of olive or Japanese indigo.
Seersucker I never quite settled with as shirting, I think because I always find I have to iron seersucker shirts... and I simply refuse to live in a world of ironing seersucker. Too absurdist!