Arguably the reason many of us even know what solitaire is (myself included): Microsoft Solitaire, developed by Wes Cherry, an intern for Microsoft at the time, for 1990's Windows 3.0. Solitaire (yes, it's actually called Klondike in most written rules, but let's not argue semantics) was not so much a card game as it was a revolution in computing...but not in the way you might think, going by the way I phrased that sentence.
The thing to remember about Solitaire was that it came at a time when, while Macintosh users had already been accustomed to using the mouse in everyday tasks since 1984, owners of PCs still didn't quite grasp how they worked. Mice were not necessarily even present. To some users, they were still awkward and difficult to figure out. Solitaire, though, unwittingly served as a trojan horse of a teachable moment - as a computer user played, they would gradually learn how the mouse works, eventually becoming more dextrous with their pointing devices as they clicked, double-clicked, and dragged the cards around the screen with increasing precision and speed.
A real sculpture produced by Oslo design studio Skrekkøgle.
Solitaire's main ingredient to popularity, though, was that it was automatically installed with Windows starting with version 3.0 (earlier versions tended to include a different game, Reversi). Taking up a combined total of 344 KB, most Windows users had no reason to remove it afterwards...except for corporations and companies who (rightly) worried about productivity loss on the job. (According to Wikipedia, there has been at least one high-profile firing, directly attributed to Solitaire.)
What's most interesting about Windows Solitaire, though, is that it also serves as a perfect example of what DLL files are for. The DLL, or Dynamic Link Library, is a file that contains resources or specially prepared executable code that many programs should have access to. In modern Windows, DLLs tend to be things like Visual C++ runtimes, DirectX libraries, and common windowing functions. In Solitaire, Windows refers to a file called CARDS.DLL, containing the graphics for all 52 cards as well as all the card backs and associated animations (and, if I remember right, the drawing algorithms for card stacks). This is mostly an intrinsic part of how Windows and DLL files worked at the time; it's better for memory management if the EXE doesn't have to load a bunch of resources out of itself, and only calls the resources out of the DLL file when they're needed. But CARDS.DLL being a separate thing was also beneficial to other Windows card games that came later, such as FreeCell (bundled with the Win32s 32-bit libraries), Golf, Cruel, and TriPeaks (part of the Microsoft Entertainment Pack series). Since CARDS.DLL handles drawing the actual cards, anybody who writes a card game for Windows does not need to provide their own graphics or drawing code. As a result, even shareware card games like Forty Thieves, Canfield and Constitution were able to keep their file size down considerably by referencing a file that, due to its inclusion with every Windows installation, was guaranteed to be on the system.
Around 2015, Susan Kare designed a new Joker card for a physical version of her famous Windows Solitaire deck, distributed by Areaware.
CARDS.DLL was also important from an artistic standpoint. Solitaire's famous deck was drawn by computer artist Susan Kare, the mother of pixel art, who at that point had famously drawn the operating system icons for Apple's Macintosh back in 1984. Kare was tasked with drawing the familiar French-style playing cards in a resolution and screen size that did not afford much detail, but required clarity with no ambiguity. Of course, by 1990, this was something which Kare was already very well acquainted with, having drawn some of the most expressive images to ever occupy a mere 24x24 pixels. The resulting cards became so well known, in fact, that they could even be bought as a physical deck, a perfect example of art that goes full-circle, from traditional French patterns, to computerized images (in only 16 colors), back to physical cards. Sadly, the physical cards don't feature the fan-favorite animated castle or robot designs, but what could you really do about that?
Kare's cards have such a legacy, in fact, that Solitaire - and CARDS.DLL - continued being included with every version of Windows all the way up to Windows XP. Windows Vista and onward still contain some version of Solitaire (and while Windows 8 and 10 do not directly include it, it is still accessible through the Windows Store, as the downloadable Microsoft Solitaire Collection), but CARDS.DLL has not been included since 2007. But considering that it was "born" in 1990, that is a solid 17 years of service for a file that, by that point, was so ridiculously compact that the vast majority of Windows users did not even realize it existed, let alone that it was still being used.
"Father, I cannot double-click the card."
While Solitaire didn't outwardly appear to be changing much over its 17-year lifespan, there were small changes being made to the code over the years. The classic winning animation, with its cascading and bouncing cards, that had originally played as fast as it possibly could (even being used as an informal benchmark test back in the early 1990s), soon became such a blur on modern machines that it was reprogrammed to have a speed limiter. By Windows 2000, an undocumented auto-play function was added, so players needed only click the right mouse button to send cards to the foundation piles. Windows XP replaced the card backs with newer, higher-color artwork. But for the most part, Solitaire remained more or less the same program for 17 years, and that is a lifespan that very few other computer applications can boast.
From a cleverly-disguised tutorial tech-demo, to a cultural icon, with the kind of longevity that might make any other program jealous. Even though the actual game of Klondike is much, much older than Windows (or even the concept of the computer), I'd say Solitaire is perhaps the biggest reason why people still care about it.