(Apologies for any odd grammatical errors/typos – this post was typed from a mobile phone.)
If I can give one suggestion to anyone interested in game design/development, it is this:
Play tabletop games.
By tabletop games, I mean board games, card games, pen-and-paper RPGs, and anything else you can think of. The amount you can learn by playing these games and analyzing your sessions is simply staggering.
Board games can show you countless examples of game mechanics, showing you how well/poorly some can interact, how they influence players’ actions, and ultimately how fun they are. Some will show off the value in simplicity, and others will engage you and show the enjoyment that comes from depth or complex strategy.
Card games typically involve competitive gameplay, and give many of the same benefits as board games. Additionally, you can learn a lot about games’ pacing and flow from them. For example, A game of Magic: The Gathering can be an incredibly fast-pace race to kill off your opponent, or it could be a slow grind to wear down your enemy and lock down his actions. The level of variety and modularity possible in one game also means that cards can cover just about aspect of a game you want to test if you are looking to prototype mechanics (at least, so I have been told by a few people who have tried it; your mileage may vary, they may not be the best tool for the job, etc.).
Tabletop RPGs can introduce a lot of narrative to what might otherwise be “just gameplay mechanics”. They can teach you proper pacing, story, strategy… really, most of what has been mentioned above. They also happen to be one of my favorite hobbies!
Basically, what I’m saying is this: don’t limit yourself just to video games to learn about games. Broaden your horizons; experiment a little. Even if what you learn does no translate over to video games directly, you’ll have had a chance to look at and experience games from an entirely different angle.