Technically, the vast majority of printers, whether ink jet or toner based, are still dot matrix printers. They're printing dots close enough together that the visual acuity of the human eye congeals the dots into characters, strokes and lines. However, the original dot matrix printer - where pins push against a ribbon and deposit ink on a paper - are still in use in a lot of businesses.
This printer technology was really the last generation of 'impact' printers, which are the venerable descendents of Guttenberg's original printing press - ink is put on a transfer agent, and it's then pressed into the page. Dot matrix printers were originally doing this with 9 pins of about 0.5 mm each, and grew out of the original punch card methods of getting data out of computers.
The advantage of dot matrix printers originally was that they could produce graphics other than text; back in the 1980s, it was not uncommon to have a 'graphics' dot matrix printer, and a text 'ball-and press' printer, which used a mechanism similar to an IBM Selectric typewriter to produce 'typewritten' documents. The flexibility, and later speed, of the dot matrix printer eventually relegated the ball and press model to irrelevance, particularly as the 24-pin models came into the market in the late 1980s and early 1990s.
24 pin color dot matrix printers came into the market in the mid 1990s, and were the first real attempt at putting color printing in the hands of consumers. They were quickly supplanted by ink jet printers (which did a better job of mixing colors and getting exact hues and colors out of pigments, and were faster on printing color to boot), and this eventually moved ink jet printers into general consumer products - even though their cost per page for a black and white document was significantly higher (and still is higher) than using an impact printer model with ribbons.
The real killer of the consumer dot matrix printer was the laser printer, which have experienced a hundredfold decrease in their costs and a significant increase in their capabilities. Once laser printers started to plummet in cost, the dot matrix printers were supplanted in turn; what was once a ubiquitous piece of office equipment is now regarded as a charming and quaint apparatus seen only in 'period pieces' about the Cold War...until you encounter them in a modern business.
Most modern businesses aren't holding on to these printers out of nostalgia. They're holding on to them at increasing expense because these types of printers work best for multi-part forms, where the impact of the print head creates the page handed to a customer and also the 'carbon copy' or duplicate for their own mechanical record system. These forms are still required in many cases by regulations and legislation dating back to the 1970s and 1980s - there are a surprising number of sectors of business where digital forms management is flat out not allowed, including working for the NHS in some cases.
Another realm where dot matrix printers reign supreme is on routine check generation. Many of the forms that print out checks to send to people have to have those checks printed on dot matrix printers, largely because segmented, large run forms with pre-perforations, are orders of magnitude cheaper than the alternatives.
Which leads to a problem for those businesses that have dot matrix printers - there aren't many companies making them any longer, and while the machines are durable, they're still mechanical devices and subject to wear and tear, and finding companies that make spare parts - or even ribbons - can be a challenge. But they are out there, they are still manufactured and can be found - it just takes a little extra effort to get what you need.