Martin ukuleles are some of the most sought after ukuleles around. There are many avid collectors of Martin ukuleles around and people who refuse to play anything but Martins.
Martin started producing ukuleles in 1916 and were the largest producer of ukes
There are a number of different styles (from style 0 to style 5 - but there's no 4). Generally speaking, the higher the number, the higher the price.
More knowledgeable sellers will indicate which style the Martin is. However, less well informed sellers, such as on eBay or in junk shops, will often not know what style the uke is. In this case, it's worth being able to identify which type of ukulele it is and how much it might be worth so you can tell if you're getting a bargain.
Martin stopped making ukuleles for many years. But with the new boom they're back on the bandwagon. To begin with they started by releasing new models. They were not all that well received. So they've reintroduced the old models. Which is definitely a good marketing move. Whether the new ones match up to the quality of the old ones is an area of dispute.
This video, by ukulelezaza, has three different styles of Martin ukulele. From the beginning: Style 0, 1960s Style 1, 1920s Style 2, 1940s Style 3
Dating Martin Ukuleles
Again, there you can go into minute, recondite information in this area, but their are two easy to spot features that will help you work out or confirm the Martin's age:
Peghead: The earliest Martin ukuleles (before '33) have a stamp on the back of the peghead. After this, they had a decal on the front (there was a slight overlap in these).
Soundhole: Inside the soundhole you'll see a stamp. If you can see the words "Made in USA" the ukulele was produced after 1966.
Martin Made Ukuleles
As well as making their own ukuleles, Martin also made ukes for other manufacturers such as Oliver Ditson. These ukuleles are identical to the standard Martin ukuleles apart from the maker stamps and decals.
Because Martins are so sought after, some sellers on eBay resort to shady tactics to get their ukes in front of buyers. One way you'll see regularly is people advertising the uke "w/ Martin strings" in the title. You see ukuleles refered to as 'Martin style' - even when they clearly aren't (Kiwaya are an exception to this). Another is people speculating that the ukulele is a Martin - it rarely is. Martin's are almost always stamped. Personally, I wouldn't buy anything from a seller that uses such desperate tactics.