Each era of gaming has its own unique gameplay feel & quirks, and they're all worth playing if your in the mood for that generation's style.
What I call the 'vintage' and 'classic' eras of gaming (so from the Odyssey to 16-bit) excel in fast-paced, arcade like gameplay. Things where you're not really worried about story, but pushing up that score bar. The Vintage (pre-NES) stuff works best in concentrated bursts... you get your gameplay high almost immediately, but the simplistic nature of the games means tedium can set in faster too. The Classic (8 & 16 bit) games hold up better for longer play sessions, as the added processing power allows for more variety of environments & gameplay- plus, most games here now have endings, giving you an alternate goal over score.
The 'neo-classic' era (CD based consoles, plus the N64, up to last gen) is the era of exploration. This is when we see collect-a-thon platformers and open world games start to dominate, plus it's when PC style adventure/point and click titles really start migrating over. Playing in this era rewards those who want to take their time with a game, and look in very nook and cranny for content.
The 'Modern' era (last and current gen, the 'online' consoles, if you will) is the age of multiplayer, and gaming as an 'experience'. We've plateaued on graphical prowess- progress can still be made, of course, but it's slowed down enough to be difficult to notice. A lot of games, as a result, seek to make their mark in other means. Strong storytelling has become commonplace, online multiplayer allows for a new form of interactivity, and experiments in design have lead to some truly gorgeous titles. If you're one of the 'games are art' crowd, who wants to see the boundaries of what we call a 'game' get poked & expanded upon, then the current market is doing just what you like.
These are not mutually exclusive breakdowns... there's nostalgic throwbacks & titles before their time in every generation, and you can bounce around between gameplay styles as you see fit. But if you lean towards a specific type of game, you'll likely have a preference for one of these groups. I really enjoy the artsy-fartsy indie stuff of today, so I do play a lot of modern. But that doesn't mean I don't sometimes just want to sit down with an a pile of Atari carts, and throw dots around to get a high number once in awhile. Or maybe get an anthropomorphic animal to mosy around a green valley looking for shiny things. There's merit all around.