I know he adopted that hat as his signature look as a gimmick to be the tallest dude in any 100 mile radius, but he always seems to have been able to buy a new one of these hats in town without much fuss. Was it a fashionable hat, or at least a common one, during his political life?
Yes, it was in fashion. Lincoln's hat was just a top hat, and it was worn by many presidents. Top hats were worn generally by the upper class and had silk lining, you can even see JFK at his inaguaration wearing one. Here is an image of JFK and Ike rocking some top hats. Lincoln's signature stovepipe hat can be thought of as a good example of branding in politics. I don't want to break the twenty-year rule of this sub by bringing up other political apparel (Trump's hair, to be fair, has to be at least that old) but a politician with a signature look can help make them memorable. I can't remark specifically about the length of his hat, but they were custom-made silk top hats worn by upper-class males. The black band he wore around the hat was put on in mourning for his son Willie. He was known to carry papers in his hat, as well.
Top hats of one sort of another were considered an essential part of men's formalwear through the 19th century and continued be used into the 1940s and 1950s. That said, the exact style, shape, and construction of top hats changed over time.
"Stovepipe" top hats of the 1850s and 1860s tended towards a taller shape with straighter sides.
This photograph shows a "stovepipe" top hat of the 1860s similar to the sort that Lincolcn was known for. Notice the wide band and the nearly uniformly straight brim.
Linclon, being uncommonly tall, looked rather better in a 8-inch tall top hat than most people might have. This page has a photograph of the actual top hat President Lincoln was wearing when he died: http://www.civilwar.si.edu/lincoln_tophat.html
