22-year old here, soon to be 23. My interest in Atari stems from a few interrelated factors:
Lack of time. As my days grew more stressful, life got busier in college, and I got a girlfriend, the time to play longer, more involved video games evaporated pretty quickly. On a tight budget, I figured what the hell – I've always liked arcade games and shooting for high scores, and I've always enjoyed older video games, so I might as well give Atari a shot. Glad I did, too: I've gotten many hours of enjoyment out of the system that bennybingo sold to me for cheap years ago (gorgeous little 2600 Jr.)
Comic books and budget. With my lack of time also unfortunately came a lack of time to read longer novels. Also, as a humanities student, I was reading upwards of 400-500 pages a week of dense material. Given how tired I was at the end of each day, I started to turn to comic books to get a bit of reading in before bed. Now I'm totally in love with the medium, and I've read many dozens of fantastic stories contained in both Western comics and manga. In turn, given this new hobby, my budget for video games also dwindled to virtually nothing. 2600 games are generally dirt cheap compared to modern video games (even 3DS games are, what, $30-$40 a pop?!) While I use a Harmony Encore now and have sold nearly all of my old carts, so I'm not a "collector," the price is great for how much content you get with the Harmony.
High scores and comparative simplicity. While I still love a good story, I just don't have the time for RPGs or similarly involved, long games anymore – hence my growing interest in playing for a high score. Playing a 2600 game is so damn easy – press the "on" button, select a game from the Harmony menu, and you're off to the races with one button and a joystick. Manuals aren't even needed for many games; you can figure them out on your own pretty quickly. Well, that is, until you want to try some of the alternative game modes or really dig into the core of a game. Might have to hit up the AA manual archives for those.
Overall I'd say my tastes have changed as I have grown older, and I love firing up some tunes or a podcast and playing my 2600 for an hour or two to unwind at the end of the week. Timeless fun