I'm a big fan of the Brooks Brothers non-iron shirts (extra-slim fit, for me). Awesome fit, they don't wrinkle easily, and when they do need ironing, they are super-easy to iron. Less expensive shirts I've had tend to wrinkle more and are difficult to iron.

I cover them with those plastic dry-cleaner bags, fold the sleeves diagonally across the torso and smooth it out flat, then pack them in my tri-fold garment bag, or the suiter bag if I'm using my convertible travel pack. They almost always arrive wrinkle-free. Occasionally I do a little touch-up ironing at my destination but that's more due to me being very picky about a well-pressed shirt than anything else.

Watch for the sales they have at Brooks a couple times a year. I only buy them when they go on sale when I can get them for $44 or less.