I almost never carry one with me while diving. I swim on my back at the surface, or I breathe from my reg.
I feel the snorkel on the mask strap is a mess : it's an entanglement hazard, it's not comfortable, it prevents from being streamlined, out of the water it makes the storage of the mask more complicated and finally it increases the risk of wearing/breaking the mask strap. I hate carrying a snorkel on the mask strap.
It would be nice to carry it in my BCD but I almost always feel it takes too much space, so I tell myself "it will be OK one more time without it" and I usually leave it in my bag.
If I feel really scared that I could go adrift for a long time, then I carry the snorkel with me (in a pocket or tied somewhere but never on the mask strap) or, more likely, I don't go for this dive. But sure, one never knows ...
Once I saw a diver trying to climb the ladder back to the boat with his snorkel in his mouth, sea was choppy and he fell back and almost drowned - he was rescued by someone - sometimes it's much better to trust your reg more than your snorkel. (edit: this is anecdotal - nothing wrong with the snorkel itself. end edit)
Same story than Vladimir happened to me with a pod of dwarves orcas.
Once I went (without scuba but with wetsuit, mask and fins) from the shore to assist a snorkeler who was having some trouble, but my snorkel wasn't in my box so I did without but that was not much fun - now if I am diving from the shore I make sure the snorkel is at least in my box/bag.
Sooner or later I will probably miss my snorkel again - I hope it won't be a real issue then.
Thanks DCBC to rise this subject and give us matter to think about.