My first game was the Mario/Duck Hunt. But I think that was the only platform series that I have really enjoyed.
To me I was obsessed with the original NES Zelda, and the Dragon Warrior/Dragon Quest series. I loved the epic fantasy theme, the open world, and the exploration elements. In those games there is a huge wide world that your character lives you have a heroic journey to undertake to save it. I could go on and on, but what about you??
I also love the Zelda series and remember playing one of the Dragon Warriors for NES. Played RPGs as well such as the final fantasy series and some others (Lufia? don't remember the others as well).
So I guess what I liked about them is the open-world type exploration. In both the Zelda games and most RPGs you can kind of go at your own pace—explore every nook and cranny looking for secrets and loot, or head straight to the next dungeon, boss, or quest. I usually chose the former first, explore everything, level up and/or find helpful items. But it also made it exciting when I chose to risk it and push on before I thought I was prepared enough.
I also loved being able to see future secrets and getting exciting when getting the item required to get there. Zelda did this a ton - see a rock blocking a path early on. Later get a hammer/power bracelet and you can backtrack to unlock that secret.
I have been thinking a lot lately about what makes a game fun. Now that I am getting a little better with pixel art and Construct I realized I haven't even touched on making the projects fun. So have actually been thinking about this lately.