I've always found Atari's decline to be an interesting subject in video game history. Atari, after all, is the company that made home video games big in the first place. They brought PONG home. They didn't have the first programmable video game console, but their 2600 is the first successful programmable video game console. Technically, the Atari of classic video gaming fame is three companies: Atari, Inc, was founded in 1972 and split up on July 1, 1984 into Atari Corporation and Atari Games. Atari Corporation went defunct in 1996, being acquired by JT Storage, and Atari Games was bought by Time Warner in 1993 and sold to Midway in 1996, being renamed Midway Games West by 1998. Atari Games also changed their logo from the classic "Fuji" logo in 1996.

In effect, Atari Corporation's closing date is pretty clear cut: 1996. Atari Games, on the other hand, was a process from 1993-1998 - 1993 being when they became a subsidiary instead of an independent company, Tengen was closed up and their home video games sold under the Time Warner Interactive label. 1996 is when they were sold to Midway, who changed the logo and, a couple of years later, retired the Atari name.

The "Atari" name is still active, but is not a continuation of the original company; rather, it's owned by another company (Atari, SA), which was founded as GT Interactive in 1993.

It always surprises me just how late Atari remained relatively successful. To many, it's seen as a company that lost relevance around 1983-1984. And while the "golden age of Atari" did end around that time, they did a lot more in the latter half of the 1980s than is often realized, and it was the 1990s when they went into steep decline and ultimately out of business. I found a thread from 2010 that detailed how Atari's home consoles fell further and further behind the times, but let's look at what Atari did as a company as a whole. They competed in three areas for most of their history: home video games, arcade video games, and home computers.

In the late 1980s, Atari was still relatively healthy. Their home video game division included the 2600 Jr., the 7800, and the XEGS, as well as the Tengen division selling NES games. While they were a far cry from their dominant position in the home video game market in the early 1980s, they still held a substantial share of the home video game market, about 10-15 percent with hardware as well as being a prominent publisher for the NES. They released a steady stream of arcade titles like Gauntlet, Klax, Paperboy, and Marble Madness in an arcade market that, again, was a far cry from its early 1980s state but still relatively healthy. Their 8-bit computer line was still going and selling reasonably well, and the ST was very successful in Europe. I consider the period from about 1986-1989 to be Atari's "Silver Age", not as good as its golden age, but still decent. At the end of the 1980s, they came out with the Lynx, which was nowhere near as successful as the Game Boy but did become the first luxury handheld console.

Right around 1990, Atari's fortunes began to go south on all three fronts. In the home console arena, the 7800 and XEGS faltered, and were discontinued very early in the 1990s. The 2600 had lived out its life and was discontinued at the same time. By 1991-1992, Atari was left with the Lynx and Tengen in this area. The Sega Game Gear launched, providing a better option in the color portable market.

At the same time, the Atari computers (as well as Commodore) were being squeezed out of the market as the forerunners of the modern Wintel platform (IBM architecture / MS-DOS) was rapidly becoming the standard for PCs. The market was headed toward IBM/DOS dominance; Apple hung on but became a niche product with only a few percent market share.

On the arcade front, few games were produced after the early 1990s, and Atari Games themselves were bought out in 1993.

By 1993, Tengen was discontinued, Atari computer production stopped altogether, few arcade games were coming out, and the Lynx was fast declining against the Game Gear and Game Boy. The Jaguar console was a sort of "last-ditch effort" released that year, with very few games available at launch. Atari had gone from fairly healthy to nearly dead in just a few years.

The Jaguar wasn't much more capable than the Genesis and SNES; if the SNES was the benchmark for 16-bit and the PlayStation the benchmark for 32-bit, then the Jag might have been 20-bit. From what I understand, it was about as powerful as an SNES with a Super FX chip. However, it was far cheaper than the 3DO, and may have been as successful as the 3DO (admittedly, that's still not a roaring success) if it had a few good games near launch in 1993 with a wide range of good games available by the holiday season of 1994. Instead there was a trickle of games the first year and most Jag games came in 1995 when the Sega Saturn and PlayStation were launching. Sam Tramiel actually thought the Jaguar could compete with the PlayStation. The Jag had about as much chance against the PlayStation as a paper McDonalds cup against a 1982 Cadillac.