I have shapers, and I use them. I also have a milling machine that I use. In my opinion, here are the advantages/disadvantages of shapers:
Advantage: You can buy ones in the 12 and larger range cheap, and the larger end of that range can remove metal at a high rate, higher than a BP or it's clone.
Advantage: They use a cheap tool that is easy to sharpen to remove that metal. You can do angles, including dovetails, fairly easily with a cheap tool on a shaper.
Advantage: If you add some switches to the crossrail to shut it down at the end of the cut, you don't have to babysit it. I havn't done this to mine yet, but it is something I plan to do. It's one of the advantages of a CNC machine, you can set it doing a job, then go work on something else.
Advantage: You can do internal keyways/splines, including blind splines (you do need to cut a chip relief). This is a capability that I most hear people needing shapers for now. For very small quantities making a broach is too much trouble. It's only worthwhile to the repair shop or the hobbyist, for production this would be done with a wire EDM or a broach.
Advantage: They are cool.
Disadvantage: Small ones are expensive. I know you guys on the east coast can probably still pick up and Atlas 7B in great shape for 300 bucks, but the same example out here will cost you a grand.
Disadvantage: They are a 2D tool. Think of a linear version of a lathe. You can't produce a pocket with a shaper alone. They are good at things like flat surfaces, slots, dovetails, gears, splines etc. I wouldn't rely only on a shaper for my shop, and I wouldn't get one before a milling machine unless the deal was too good to pass up.
Disadvantage: The big ones take up a lot of space. That ram has to have room behind the machine, unless you plan to cut a hole in the wall.
Disadvantage: They can be quite heavy. Depending on when they were made, a 16" shaper can range from ~1500 to around 4000 lbs. Generaly speaking, the newer they are, the heavier they tend to be. A 24" Cincinatti HD will tip the scales around 7000 lbs, but I consider that to be out of the league of all but the most hardcore hobby machinsts.
Disadvantage: There are a lot of things that need to be done to set them up, compared to a milling machine. You have to set the stroke, then the tool position, the toolhead setover, the toolhead angle and the autofeed. Depending on how old it is, you will probably have to oil about a thousand oil holes, or a few less if it is a newer machine. This may or may not be a disadvantage, depending on how you look at your shop time.
I use mine, not as much as the lathe or mill, but but they do get use. It all comes down to whether you want one or not. They seem to be an ideal machine for the home shop guy, since they can generaly be had cheap, and use cheap, easy to sharpen tooling. It all depends on if you have the space and want one. They seem even better every time a destroy a $50 carbide end mill in my CNC machine.
As an aside, if you do a bit of searching on the internet you will find they still make new shapers in India and China. From what I understand, they are used by repair shops and small job shops in third world and developing countries because the tools are so cheap, and can be easily sharpened with a simple bench grinder. Labor is cheaper there, so the longer set up time and (possibly) longer run time don't make as much difference.
Also, there is a bit of a misconception that they are slow, mainly due to only cutting for ~ 2/3 of the stroke, but a 16" shaper should be able to match the metal removal rate of a milling machine that is typicaly found in the home shop, namely the BP or one of it's clones. I saw a picture of a large one (32" Rockford, I believe) taking a 2" deep cut with a .060 feed in mild steel, the chips were curled strips of sheet metal. I'm sure they were blue, but the picture was in black and white. Ok, enough for today.