For a long time, Pokémon was probably the one that I enjoyed consistently throughout all of the Nintendo franchises. Even during the times I didn't play, I did follow official announcements, and I also occasionally watch the anime. So what was great:
With some exceptions, the reality of the world it is based on.
The very fact that Pokémon's geography didn't start out willy-nilly like other Nintendo games is something special. Sure, Earthbound may be another game that is based on our modern, realistic world, but Pokémon pushed this further by actually basing their regions from real-life Japan, USA, and France. This is why I love XY and GSC for actually creating a region that is as fantastic as necessary, but as realistic as possible. (It is also the reason why RSE/ORAS is the game (and the only game) that I dislike.)
The balance of the story
As a child, I found it simple enough to be approachable, unlike Fire Emblem. I guess, with some exceptions, I generally like lighter games, and I only started to appreciate deeper stories like Fire Emblem later in my life. (I was in middle school when I first started to play my first FE game, which was Binding Blade.) On the other hand, it is also potentially deep - I have been running a series of headcanons over at Bulbapedia, because the simplicity of the story allows this.
(For example see one of my headcanons at Bulbapedia here: http://bmgf.bulbagarden.net/blogs/72744/category2042/ )
Not having the stupidity of Mario also helps - everyone is competent in one way or another. (This can also be potentially said for the majority of FE Characters too.)
Misty and Kris (Sorry Lilina and Caeda)
Witnessing the first female main characters that is anything other than a damsel in distress, AND that is not Samus, was really refreshing. Caeda (FE) and Paula (Earthbound), I only got to know later on. Lilina was obviously not around until FE Elibe came out, which I think was right before Pokémon RSE. At the time of Pokémon GSC's release, I didn't even know about Fire Emblem, and I only heard the name for Earthbound, and only started playing after the GBA remake came out. Zelda only caught my appreciation since Twilight Princess (and her Flaming!Light Arrows were awesome). Peach I actually have a hate towards - for still being an largely incompetent damsel even after Smash Melee came out, and despite this continue appearing in later Smash games when there are better female characters.
Ash Misty and Brock
While I won't deny that the anime has ended up with problems with its story and characters later on, you gotta admit, who didn't enjoy watching Ash, Misty, and Brock going around Kanto (and maybe Johto too)? I'd be kidding myself if I said that the anime didn't introduce me Pokémon. At least it is in a separate continuity to the game, and there's the Special manga for more mature audiences so you can switch over easily once the anime loses your charm, and let TV Tokyo do their job of introducing the franchise to the children around the world.
