Often called braces, gallows, or galluses, suspenders first appeared at the end of the eighteenth century. Men began to wear their breeches and trousers higher (at or above the "natural" waist), and they needed suspenders to achieve this fit. Some hundred years later, waistbelts overtook suspenders but also functioned to hold up trousers, by tightening the waistband. Without such things, pants slide down closer to the hips near where most of us wear them (without belts) today.
This 1790s English satire shows an early pair of "Nete Gallows for Breaches" hanging in the shop of "Simon Snip."
(c) The Trustees of the British Museum. 1935,0522.1.204.
In the nineteenth century, men who worked without vests or coats often displayed plain or fancy braces, like those worn by these Civil War soldiers or shown in this pairing of original and reproduction Berlinwork braces. Here's an image I picked up at a recent antique show in Kutztown, PA. It's a great example of how late nineteenth-century men used suspenders to raise and hold trousers above what we think of as the modern waistline. And don't miss this dapper gent's checked trousers, knit shirt, and bandanna.
Tintype, 1870-80s, Author's Collection.
Sadly, it seems that it may be some time until those of us in the mainstream can adopt stylish suspenders without getting sidelong glances when we're out on the town.