My wife bought a black "Diaper Dude" messenger-style bag for me before our daughter was born, and she got an expensive designer one from a friend at a shower. The Diaper Dude bag is used almost all of the time now, because it is more intelligently designed than the nice bag. Maybe if we have a second while our daughter is still in the diaper world we will use them both at the same time, but that seems unlikely to me at this point.
My wife has a Skip Hop DASH bag in the Cherry Blossom print design as pictured below:
Not exactly the most masculine but that said, Skip Hop does have other designs which are actually pretty nice. Personally, if I'm with my little guy, I carry our diaper around proudly as it's quite obvious my wife was the one who chose this bag!
I have this one too! I love that brand and use it now as my own work bag that also happens to have diapers and binkies in it. I have a smaller clutch type that held one or two diapers, a changing mat and a wallet that was perfect for times I didn't want to carry luggage. It's quite feminine, but my husband has proudly slung it over his shoulder on trips to the doctor and such. I suggested getting him a backpack, but he would rather use what we already have.