The long, black, leather trenchcoat is one of the most practical foul-weather coats available. Leather has a number of advantages over many other types of weather protective material, the only real disadvantage being that you have to take care of it (although that isn't very difficult).
Leather's greatest quality, well known to leather jacket wearing motorcycle enthusiasts everywhere, is that it stops wind chill completely. Whether cruising down the interstate on your Harley-Davidson at 70 mph or just walking across the parking lot in late Autumn, the biting cold of the wind will not penetrate the thick layers of cow hide wrapped around you. Many leather jackets and coats also have removable liners for extra warmth. Of additional interest to motorcycle riders and people who get into a lot of knife fights is that leather is tough, and provides some level of protection.
Following in a close second is treated leather's waterproof quality. Combined with the classic trenchcoat design which covers your body from the neck down past your knees, you don't really even need an umbrella. Of course, the trenchcoat was designed to be warm and waterproof even before they started making them out of leather. Trenchcoats were, as the name suggests, invented for use in trench warfare in World War I to keep British army officers comfortable in the wet and miserable conditions they spent days at a time enduring. They were so effective (and stylish) that they moved into the civilian market soon after.
Basic black is, of course, a timeless color. It goes with everything, it's appropriate for almost any occasion, and despite fashion magazines' occasional reports that something else is the "new black", it's unlikely that any other color will ever find as wide-ranging a niche as black. Going to a wedding? Black is safe. Funeral? Black is all but mandatory. Evening cocktail party? Can't go wrong with black.
That said, there are two disadvantages. First, people who have never seen a real goth before tend to group me into that category. You simply can't explain to those people that it takes a lot more than a black coat to be goth. I wear it because it's practical, comfortable, and stylish. Not because it's a reflection of my dark, tormented soul.
Second, you need to take care of it. Leather is flesh, just like your skin, and unlike synthetic materials needs some TLC to keep it in good shape. Never store leather in a plastic bag (it sweats), never pin anything to it (the pinholes stay, unlike in woven fabrics), and don't leave it lying out in direct sunlight all day (it'll dry out and crack). Occasionally applying a protective lotion to the leather will keep it shiny, moisturized, and looking new, and a good waterproofing treatment once a year is necessary if you want to use it to keep the rain off.
On the other hand, it is easier to clean most dirt and spills off of leather than woven fabrics. They tend not to penetrate the outer layer, and can be wiped off easily with a damp cloth.
Wntrmute points out that leather coats, especially ones bought from smaller retailers, often come with long warranties. This is important when you're shelling out a few hundred dollars for a nice one that you hope will last a long, long time. Warranties usually cover lost buttons and damaged stitching, as well as other services to keep your leather looking nice.