A vintage Martin guitar is cherished for many reasons, not the least of which is the storied history of the Martin Guitar Company itself. Founded in the early 19th century in New York City by C. F Martin, Martin Guitars soon relocated to Nazareth, Pennsylvania-where it would soon be known as one of the premier American guitar makers. For some, Martin is still the standard bearer when it comes to steel string acoustic guitars, and this reputation has been earned in no small part because of the company's accomplishments in the early 20th century. Martin guitars has been a "family affair" from the beginning - since 1833 the company has been run by the descendants of C. F. Martin, still to this day.
Martin was the first company to feature the now-common Dreadnought body shape and scalloped bracing (where the top of the guitar's bracing is "scooped," supposedly allowing for greater bass response). And while Martin did not invent so-called "X-Bracing" they certainly help popularize it. Never one to rest on their laurels, the company has continued to embrace new technologies such as acoustic/electric integration and PLEK-machine setups.
Martin has made a wide range of guitars in its nearly 200 year old history, but when people talk about aquiring a vintage Martin guitar, it's really instruments from the early 20th century that they're likely talking about. These are sometimes referred to as "Pre-War" Martins (i.e. pre-WWII instruments) - the D45 model. They are noted for the usage of Brazilian rosewood since Indian rosewood was used after the war. Other innovations by Martin during this time include the 14-fret neck and the Dreadnought body shape, possibly the most common and popular acoustic body shape still in production (and widely copied).
If you're fortunate enough to live in an area where there is a lot of selling amongst private individuals, you can always find guitars for sale on Craigslist or local music stores. There's also no shortage of vintage Martins for sale online through sites like eBay or Reverb. Other trusted online retailers include Gruhn's guitars and Elderly instruments. You want to make sure that you buy from a reputable dealer who can identify and vouch for the Martin guitar you want to purchase. If you purchase a vintage instrument solely from pictures and other online media, make sure that the dealer or individual has experience shipping vintage instruments and that it is insured for the full value.