I use this ASICS Long Sleeve Athletic Shirt for running.  This shirt is nice and soft but I feel that the fabric is a little too thin.  The plus side of being thin is that it is extremely lightweight.  The size runs a little big.  I Have a 41 inch chest and weigh 180 lbs, the large was way too big for me.  I normally get workout shirts in a size large but I think I might have been better off getting this one in a medium.  A word of warning, do not let Velcro touch this shirt!  It will damage the shirt.  I threw my weightlifting gloves inside my gym bag and the Velcro damage to my shirt.  Nothing bad but just thought I'd mention it.

Pros:
Lightweight
Good moisture control

Cons:
Size runs big.  Get one size under your normal shirt size.
A little too thin