I think Pokemon games are successful because the gameplay tends to go beyond just battling.
Here's a short list of what I liked about the games:
- Trading (Wifi)
- Battling
- Mixing Poffins/PokeBlocks
- Doing Pokemon Contests
- Making and sharing secret bases (Ruby/Sapphire/Emerald)
- Running around underground, Mining, and making secret bases (Diamond/Pearl), although I never quite understood the capture-the-flag thing
There really wasn't much need for endgame content because there was so much to do if you were able to play with a group of friends. Having said that, it's safe to say that I never really played the game competitively. I didn't catch-em-all, breed much, or raise the strongest Pokemon. I played because it was a fun way to spend time with friends. I think that's the main appeal the game has to a lot of non-hardcore gamers.
So...more specifically, here are a few other things I liked about the games:
1) Day/Night Feature: This is something that started in Crystal Version. It was revolutionary to play a game that had such an obvious connection to the real world at the time. You catch certain Pokemon during the day or at night, and do certain events depending on the day of the week. In Diamond/Pearl and Black/White, they took this feature to the next level by adding the four seasons. But Crystal also introduced to the series the...
2) PokeGear: This device has many spin-offs in later games, but basically it combines the map with other cool features such has a radio and a cell phone. With the radio, you can actually tune in to different stations depending on the time of day and listen to the music for certain benefits/events. With the cell phone, you can for the first time battle trainers you've already faced in the game. In Emerald version, you can even battle Gym Leaders again. Emerald is actually my favorite game because of the...
3) Battle Frontier: As you know, each generation typically has two main versions and a third spin-off version. Emerald was the spin-off to Ruby/Sapphire, and it was the only one to include the Battle Frontier, which introduced several new ways to battle with only three Pokemon. This was the game that made strategy and tactics matter because each battle facility had different game mechanics and limitations. You had to know your type strengths and weaknesses, and strategically place your Pokemon in the right order based on this. For example, in the Battle Arena, you cannot switch Pokemon and you have only three moves before the fate of the battle goes to judging based on Mind (who uses the most offensive moves), Skill (how many of your moves actually hit), and Body (who has the most HP).
I can go on and on, but I'll just say that this site is a good place to look for all that the games have to offer, and why it has such a huge fan base after so many years. I didn't really like the anime series all that much (though I did watch them), but I have to say that I genuinely don't have many complaints because the games were fun.
What didn't I like? Well...the random battle feature. I don't know, random battles tend to bother me in any video game. Because battling trainers was usually enough to level up my Pokemon, I could get away with using Max Repel all the time (so it wasn't much of an issue).