Ok, so I know that most people haven't even thought about a Dot Matrix printer since the late 1980's. Personally though, I have always been a fan of Dot Matrix printers, primarily for their superior durability, longevity, and low cost to operate. Anybody who owns a printer, whether it's an Inkjet or a Laser, is well aware of the outrageous cost for ink and toner, sometimes being even more expensive than the actual printer itself. This is why at home, whenever I am printing something non-critical, I tend to use my old Dot Matrix printer, an Epson LX-800 from 1987.
First of all, I mentioned durability and longevity. This printer is over 30 years old and it's still printing just as good as it did back when I was a kid. You're not going to find that kind of longevity from any modern Inkjet or Laser printer today, I don't care who the manufacturer is.
The next point in favor of the Dot Matrix printer is the cost of ownership, namely ink. Unlike inkjet printers which take ink cartridges or laser printers which take toner cartridges and drums, Dot Matrix printers are impact printers, operating in a similar manner to a typewriter. Letters are made by using little pins to hit an ink ribbon against the paper, making small dots. Unlike inkjet cartridges which can cost anywhere from $50 and up, or laser cartridges which can cost in the hundreds depending on the model, you can get dot matrix printer ribbons for as little as $4. That's four dollars, not forty. Four. The ribbons last a long time too, and unlike inkjet and laser printers, they do not stop printing when you are low on ink, the color of your printout will just start to fade a little. You can even "recharge" a dot matrix ribbon using WD-40.
The downsides to the dot matrix printer are printout quality, noise, and speed. Generally speaking, they are louder, slower, and the printout doesn't look near as good. This is especially true with the common 9-pin dot matrix printers (which I have). There are also 24 pin printers which offer a lot better quality, although they cost a lot more up front.
Here you can see a side by side example of printout quality. I have also scanned each page, which you can download as a pdf here:
Now, whether or not the speed and noise are an issue really depends on you. As I mentioned, I use the dot matrix at home for causal printouts where quality isn't a top concern, and I really do not have a problem with either. Also, the printer I am using is over 30 years old. I have seen videos of newer models that are a bit quieter and faster.
The final issue against the Dot Matrix printer is the upfront cost. If you are going brand new, the cheapest model that you would want is about $200. Inkjet printers are half that or less, although you will more than pay for it in the long run with the ink. Something to keep in mind.
As I said in the beginning, I personally love and prefer the dot matrix. Certainly they are not for everybody, but if you are just doing casual printing or sending out the occasional letter, I think they are more than adequate. They are also dirt cheap to operate, and since the design is so simple, they will last for years and years.
If you are looking into getting into the Dot Matrix game, i'd suggest either finding an old workhorse on ebay, or if you are going new, check out the Epson LX-350 on Amazon. That is a model I actually plan on upgrading to at some point, so it's worth taking a look.