I'm obsessed with Heroes, and slightly obsessed with several other series.

Cyndaquil.
Hands down.
Thread over.

At the current moment, it'd be a difficult tie among 3 games.

We begin with Sid Meier's Civilization V.
It's a fantastic RTS following many empires, The Greeks, Germany, even the United States of America.
You begin in the ancient phases of your empire with but a few basic units. You found your first city- your capital - and begin to construct buildings, train units, and research new technologies. With the amounts of technologies you get, you can build new buildings, construct more things on tiles and exploit resources, and become able to train new types of units, along with a few other benefits. There are tiers of research which are eras. You go to the Classical stage, Medieval, Industrial, etc.


Next up is the lovely Endless Space.
Yes, another RTS. I purchased the game when it first came out and it was, and still is, simply breathtaking. You are the emperor of a civilization in space. You start out with two ships. One is used to colonize another planet / star system, and the other is usually used to investigate the area around the beginning star system. You colonize the planets of star systems, with varying amounts of planets and types of stars, which then you may possibly exploit to get bonus of a resource. There are four main resources.
Production- This is the obvious one, used for building ships and the like.
Food- This is one I've always found a bit tricky. The amount of food being produced by a star system leads to how much they reproduce, and thusly how many people are on the planet. (The more people, you get a bonus on each resource.)
Science- This is used to research new technologies of the four main branches
Dust- This works as a currency of the game.
The wars and battles are absolutely magnificent. It's a card game, but you watch the ships engage one another, and they actually use what you can customize them with, like torpedoes, kinetic weapons, etc.

Then finally, Starmade.
I have a bit of an obsession with space and xeno-biology, I am forced to admit. 
This game is more of a sandbox game, on-par (if not in my personal belief, better) with Minecraft. Except, you know,
It's in space. You create a ship with several things from shops, such as thrusters or shields, weapons, etc. You fly to planets and sometimes asteroids, and gather minerals, etc, to use in construction of space-stations, new ships, or to sell to go to construction of either. It's quite a well-done game and there are plenty of ships created by the community available online. Star-Destroyers, The Millenium Falcon, even. It's quite a lovely game, and even better, it's entirely free. I highly recommend all three of these games, though, I could never, simply never, choose which one i loved the most.

Graphics
   Naturally, a game run on a Gameboy can't be expected to have excellent graphics. However, compared to other games on the system, the graphics are quality. Absolutely mint graphics compared to most others. Now equipped with animations, and signs to show you where you are, you'll have a much more in-depth play-through of Pokémon.

Sound
   Like I said, not much can be expected from the system's abilities, so I can't entirely give much of a critique on the sound, however I personally don't mind and find it's relaxing, though at times, it gets slightly choppy.

Addictiveness
   The Pokémon games are fantastic and extremely addictive, almost no play-through is the same. Because of this, I am always pulled back into the gravity of this brilliant series, no matter what I was already doing. It's extremely addictive, and I love it.

Story
   The Pokémon stories aren't that great, because you really can't have a brilliant storyline following a kid who just left home to pick up a Pokémon and collect as many Pokémon as possible, though I think with the addition of Suicune and a new, shiny story, it's much better than the previous ones.

Depth
   The Pokémon games are probably one of the earliest open-world games I'm aware of. You can think about where Pokémon are regularly found, and retreat to that location if already passed, or make your way there to train and capture your new Pokémon. You can go to different places and do different things, and for this era that was brilliant.

Difficulty
   The controls are fine, and the game overall isn't very hard, though I would suppose depending on how you went through it or what Pokémon you chose to begin with, that you might have a rougher time going through and finishing, like different challenges people issue over the Internet, and so on, I myself find that Fire types are usually the easier way to go, but I suppose it's up for debate.

Overall
   Brilliant edition in the Pokémon series, equipped with an actual story, animations, and other various things I'd have problems even finishing listing, the game is possibly one of the greatest of my childhood and one of my favorite games of all time. I recommend it, it's really just a great game and I personally love it. So, have fun on your adventure to complete your Poked ex and become a Pokémon master!