The GTA series has become one of the most well-known and successful video game franchises of all time.
Based on total sales, the GTA series is only behind the Mario, Tetris, Call of Duty, Super Mario, and Pokemon franchises. In other words, Grand Theft Auto has sold more than every video game franchise except for those five (one of which is a sub-franchise of another, anyways). In fact, GTA 5 is the second-best-selling video game of all time.
However, it wasn't always the juggernaut fans know and love today. There was a time when it was a middling franchise that showcased a lot of potential and sold well, yet it also had an uncertain future.
It's important to understand why the GTA series has exploded in popularity throughout the years, and why other video game franchises have failed by comparison.
The rise and growth of the GTA series

To understand how the GTA series has become as popular as it is now, it's vital to start with GTA 3. GTA 1 and 2 were good games in their own right, but the third installment of the series propelled the franchise to mainstream levels.
This is the game that popularized the open world genre. Several top-tier video games in that genre have been released throughout the years, and that's partially thanks to GTA 3's success. This isn't just limited to GTA 3, but the video game industry as a whole.
The transition to 3D

Many video game series never quite made the leap from 2D to 3D. Some tried and succeeded, whereas others tried and failed spectacularly. GTA 3 is a good example of the former category.
It set the bar as far as 3D sandbox games go. Although its controls aren't as good as later GTA titles, the game was still a gold standard to follow compared to its competitors at the time.
Clunky controls and terrible camera angles were the norms, yet GTA 3 executed it better than most of its contemporaries. This was exceptionally useful for allowing players to explore the world, which ties into the next entry.
Freedom of exploration

One of the most noteworthy features that helped make Grand Theft Auto stand out compared to its competitors was that it encouraged players to explore the open world. There were collectibles (Hidden Packages, Rampages, weapons, etc.) that helped incentivize the player to look around every nook and cranny.
There was also the fact that the GTA 3 world looked alive compared to what gamers saw at the time. Later games would only flesh this aspect out even more, which helped make the GTA series feel so immersive compared to several other video game franchises.
It's not a linear series. Some missions are done in a linear order, but there's the occasional freedom to do a different mission before another. However, it's the freedom to not do any missions that help make the GTA series stand in a positive light.
If a player wishes to go on a killing spree, only law enforcement will try to stop them.
Controversy creates cash
It's no secret that the GTA franchise has been subject to numerous controversies throughout the years. While some controversies end up being quite costly for Rockstar Games, others only serve as minor nuisances.
In the end, these controversies helped create a forbidden image associated with the GTA franchise. It seemed cool to play something so taboo, especially when so many video games back then seemed too safe and family-friendly.
Every game introduced something new

Even the weakest game in the series, GTA Advance, helped introduce several key features into the franchise. Practically every game in the series has helped innovate something and make the series even more well-received than it was already.
As a result, the early GTA games didn't feel like lazy cash grabs like some other AAA franchises that are susceptible to such criticism. Every mainline game felt like a logical progression, with GTA 5 seeming to be Rockstar's magnum opus.
GTA 5 & GTA Online

Given how long GTA 5 and GTA Online have been on the top, it's easy to forget that an entire generation of gamers knows nothing about the GTA series except for these two games. However, there is a reason for that. GTA 5 is a license to print money; gamers will always buy it.
Everything from the aforementioned paragraphs can be applied to GTA 5 in some capacity. Even so, that's not to mention GTA Online, a truly unique GTA game. It's 100% an online game, which makes it play differently from every other title in the series.