Besides the Hawaiian koa, mahogany is considered the traditional ukulele wood. This probably stemmed from the fact that Martin Guitars built most of their ukes from mahogany in the old days. It also doesn't hurt that mahogany does offer a nice sound and good durability to an instrument such as the ukulele. By most accounts, mahogany isn't really all that abundant anymore. However, most people still consider it the cheaper alternative to koa ukuleles and you will usually find them costing a lot less than comparable koa models.
I love koa as much as the next guy and most of my ukuleles are made from koa. However, right now I do have a trio of very nice mahogany ukuleles, one in each of the 3 GCEA sizes. While they don't compare to nicely grained or curly koa in terms of looks in my opinion, I do find some of the darker colored mahogany ukes to look very classy and beautiful. The three mahogany ukes I have are the Kiwaya KTS-7 soprano, the Collings UC-1 concert, and the LoPrinzi model A tenor. Each of these ukes offer great sound and good playability. To me, a good mahogany ukulele offers a good balanced tone with nice "pop". This is most evident in the Collings among the three I have, but all three offer excellent volume and great tone. Of the three, I'd rate the Collings for having the best sound followed by the Kiwaya then the LoPrinzi. You might notice that they happens to be ranked in order of their retail price (Collings = $990, Kiwaya = $975, LoPrinzi = $550), but I assure you that's purely coincidental. If anything, I think they are priced correctly in relation to each other. And of course, you could argue that the Kiwaya is more expensive given that it is a smaller uke for only $15 less. In my opinion, the Collings and Kiwaya ranks with the best of the factory made ukuleles I've played, while the LoPrinzi is a step above a good import solid wood ukulele but a slight step below a good Hawaiian made solid ukulele.
In terms of looks, mahogany is pretty much a no-nonsense looking wood. While curly mahogany is available, a great majority of mahogany ukuleles have uniform straight grain that doesn't have a lot of variance like koa does. A lot of Asian made mahogany ukes have a ribbon pattern and are fairly light colored. From the picture above you can see that the LoPrinzi is of a lighter color with a bit of the ribbon pattern while the Collings and Kiwaya has a darker appearance and uniform grain. I personally prefer the darker colored mahogany so I prefer the looks of the Collings and Kiwaya over the light and slightly ribboned look of the the LoPrinzi.
Mahogany is very light and has great strength to weight ratio. The Collings in particular feels extremely light compared to its size. I don't quite get that sensation with the LoPrinzi but that may be because it is a larger uke so even if it's light for its size, it still has a little weight to it. The Kiwaya feels about as light as it looks. I also at one time owned a 1930's Martin style 1 soprano that felt light as a feather. It was definitely lighter than the Kiwaya, but the Kiwaya is just as loud and has a more refined and complex sound. To me the Kiwaya sounds a lot like what I expect a concert to sound like.
Koa will always be THE ukulele wood of choice, but mahogany definitely doesn't give up anything to koa in terms of sound. I think every ukulele collection could use a mahogany uke because of its sound qualities and to give a nod to tradition. The three ukes presented here are on the spendy side, but there are plenty of good quality import mahogany ukuleles offered by the likes of Mainland, Ohana, Kala, and Pono.
To see and hear a couple of mahogany ukes, here are videos of the Collings and Kiwaya.
Some "studio shots" of the mahogany ukes: