Well, what is the appeal of FPS, or Action Adventure, or table top role-playing, or farmville? They're just fun for some people, and not others. It is a hobby. What is the appeal of playing piano, or restoring old cars, or collecting stamps, or reading, or playing video games? Who cares?
but since you did ask:
claiming nostalgia is a very strange thing for me. There are some games I loved as a child, but I can't bring myself to play them again and again. It just gets boring. They are still very nostalgic, but I can't say I still play them. TMNT Arcade, Double Dragon... Lets just say the entire "classic beat em up genre"
Now, there are some games that I love as a child, but their newer chapters just don't resonate with me. Star Fox (both SNES and N64 compared to the DS/GCN versions), F-Zero (SNES/GCN compared to N64). Megaman (classic series, X series, Legends, Zero games vs. battle network). People who say that Pokemon was cool until they got to Hoenn feel this way about Pokemon.
Pokemon for me is more than just blind nostalgia. For me, Pokemon ranks up there with Legend of Zelda (series), Final Fantasy (series, up to X because I haven't played the games after X [I don't have a PS3 or a 360. I have XII, but I can't find my PS2. I don't play online, so XI is not an option]) I know that I will enjoy every game because they are very well made games.
There is also something strange about my nostalgia, because I know I love mario games, I just don't play them.
now, nostalgia aside, Pokemon is awesome. No 2 games will ever be the same. even when you have maxed out your Pokemon's experience (while playing in game), no 2 pokemon will end up with the same stats. The in-game experience is your adventure. You catch the pokemon you want to catch. You battle your way through the world of pokemon your way. You an go with strong pokemon, weak pokemon, cute pokemon, cool pokemon, random pokemon. Your team is your team. You're not playing through Ash's story.
After playing the in-game story (which can take weeks if you play casual) then you can do whatever you want.
You can Catch 'em All
You can become the strongest trainer around
Or you can do what I'm doing:
I've caught them all. the full 493 National Pokedex (1 of every pokemon to fill up all of the boxes, except pokemon with multiple forms that can be boxed, because I have them all). There are pokemon from every region I just hate, and there are pokemon from every region that I just adore.
When it comes to my friends, I am the best. They don't like to battle me, because I always win. I try to make them feel better when we battle and let them take few of my pokemon out. It boosts their confidence and it makes them want to be better. They really have gotten better to. They ask me how to improve their teams, and I am happy to show them
So I am using my knowledge of pokemon to make a battle ready version of every fully evolved pokemon. Well, I just started. but I'm planning on creating them in numerical order. They aren't going to be competitive ready (because I don't care about that), but I'm planning on making them to represent the pokemon.
Fast pokemon will have 1 priority move.
pokemon with signature attacks will use their signature attack, regardless of how I feel about the move.
evasive pokemon will have evasion rising moves.
defensive pokemon will have defense rising moves.
pokemon that have a story representing their origin, their moves will represent that.
I have no intention of using Smogon for this, just bulbapedia.
Also, pokemo is just a fun way to spend time.