Also bamboo (I have Bamboo viscose (70%) and Organic Cotton (30%) shirts) - the bamboo material has excellent wicking (so much less icky than pure cotton) is super soft and I've never had a problem with odour (unlike with tech fabrics) - so long as they're washed every other day.

I've got three shirts (purchased from Amazon before a trip to SE Asia) and they've been worn every week for the last four years. Despite the odd moth-like hole they're doing great and are excellent for cycling / working out.