Founded in 1864.
The first watch Elgin made, an 18 sized B W Raymond railroad grade watch, was finished in 1867 and over the next 100 years, they went on to produce about 60 million watches. Elgin produced their first wristwatch around 1910, leading most other American watch companies by many years.
Elgin was originally called the "National Watch Company". The name never really stuck and in 1874, they changed their name to the "Elgin National Watch Company" because most of the watch trade and public were calling them "watches from Elgin". They kept that name until the late 1960s when they stopped producing watches and changed their name to the "Elgin National Industries".
Elgin was founded on the idea of mass producing high quality pocket watches using machine made, interchangeable parts. Up until around 1850, watches were made mostly by hand, which meant that if a part broke, you had to find someone with the tools and skill to make a new part. Elgin realized that there was a large market for good watches that could be sold and repaired relatively cheaply using factory made replacement parts that didn't require hand adjusting.
Elgin never made the very highest quality watches in the world, nor did they make the very cheapest, but together with Waltham (aka The American Watch Company), they dominated the vast middle ground of the watch market.
Today, collecting Elgin watches is quite popular. Because Elgin produced so many watches and produced so many spare parts, they can still be easily bought and fixed, so even a 100 year old Elgin can be used, with care, on a daily basis. While mechanical watches can't compete with quartz watches for accuracy, there is something about having a watch that ticks that a quartz watch just can't replace.
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The only ones that catch my eye are the golf ball watch and its more elegantly designed Lord Elgin range of dress watches, especially those in solid gold cases.