+1 for Icebreaker. Their fabrics are a blend of wool with synthetic materials, and they are the best shirts I've ever had. Unlike other wool fabrics they are very easy to take care of. I wash them just like cotton, no special detergents needed. Not even high spin cycles seem to harm them. (But I've never put them in the dryer, so I don't know if they would survive that).

They may be odor resistant, but for me they still get smelly after two or three days. A lot better than cotton, but not odor free.

The downsides are that even their lightest fabrics are too warm for summer, and the fabric is a lot less mechanically sturdy as cotton. It seems to tear easily. Most of my older icebreaker shirts have a few holes, even though the fabric still looks like new.