I absolutely hate ironing. There are shirts hanging in my closet for months because of it. I've found Banana Republic shirts (non iron-slim fit) to be really great when it comes to wrinkle free. I have a really hard time finding shirts because I'm pretty slim and these work great for me. I don't know how they do it but I've never ironed one the shirts and I wear them a lot! They are a little spendy for me (about $80) but I always buy one with a 30-40% coupon.

I've traveled internationally and domestically with them for work and no problems.