The primary reason why bike messengers use messenger bags is that you don't have to take them off to load or unload them. If you're continually picking things up and dropping things off all day, you don't want to be faffing about taking a backpack on and off all the time.
A secondary reason is that the flat rectangular shape of a messenger bag is more suited to the kind of things that messengers tend to be carrying (e.g. documents).
As to why the rest of us non-bike messenger types use them, there's no question that fashion is a large part. We all want to pretend we're one of those messenger free spirit types, rather than stuck in an office all day ;-)
But as well as being perceived as more cool, messenger bags are good for carrying laptops due to their flat rectangular shape. Backpacks that are designed for cycling don't tend to be as suitable for full size laptops - for example, my Deuter rucsac is fantastic for mountain biking, but my 13" laptop is quite a squeeze to fit in. (Of course there are cycling backpacks designed to take laptops, but they're not widely used from what I've seen).
Personally I'm lucky in that most days in the city I'm riding a Brompton folding bike, and I use a messenger bag that clips to the frame when I'm riding:
It's perfect for a laptop, and as well as getting the weight off my back it also carries it low on the bike at the front, which doesn't mess up the handling.
On those days when I don't have the Brompton, I'm doing a bike / train / bike journey and as the bike legs are short - and during the day I may well have to go to a client on public transport - I use a different messenger style bag. But I definately wouldn't want to use a messenger bag for a long journey, my preference would be to have the luggage on the bike, or to use a backpack.
(As an aside to the point about messenger style bags being easy to load and unload, interestingly a lot of photographers - who are also taking things in and out of the bag all day - are moving to sling bags, which can easily be swung around for access and don't have to be taken on and off for access. It's not something you think about until you're using a bag, but being able to access it without needing to take it off is important if you're in and out of it all day).