The right game for your campaign
Since this is Fandom month I want to take a chance to talk about game choice. I know I talk a lot about mostly just pathfinder and by extension 3.5 here, but there are a lot of great systems that I'm just as fond of, if not more.
When someone tells me they want to play a role-playing game in a particular setting the first thing I want to know is what game they're playing. Contrary to what a lot of people think there is no one game that can do everything. Well, okay there's GURPS, since that was kind of the point of it, but not everyone likes GURPS.
When you want to capture the feeling of your favourite franchise it's important to consider what that feeling IS. Does Firefly feel like it would easily convert to a Pathfinder game? Would have your players make members of the Justice League in world of darkness? How about a high fantasy game using the Warhammer 40K roleplaying game? Probably not. This is because the inherent tone to the game is different from the feeling you want to capture.
This doesn't mean that you can't make a very unusual combination, but it does mean you'll either be doing a lot of extra work in converting things OR you'll take ideas presented in an existing medium but give them a dramatic change in tone. Here are some examples of settings and games that mesh well:
Let's say you want to play a good old fashioned anime inspired campaign. It doesn't matter whether you're borrowing from classic anime tropes to create a new setting, using an existing one whole cloth, or weaving/mashing several together at once the ideas are basically the same. I always recommend Mutants and Masterminds for such a game, though a lot of other superhero systems can do almost as nicely. Super powered blasts? Check. Flight/air walking? Check. Super speed? Check. Absolutely everyone having unique abilities even though they stem from the same source? Double check. These are games where you can get hit by a truck and walk it off, and they pair well with the anime hero who gets wailed on, blown up, and impaled at least once per episode/issue. They keep the feel of amazing escalating power, sensational moves and abilities, tons of options, and dramatic physics-breaking moments. And yes, you could also play BESM (Big eyes small mouth), which was designed to capture such a game, but I'm still more partial to the freeform classless systems. Now some anime, like your Death Note, Tokyo Ghoul, and a lot of games more focused on narrative with lowered powered magic might be better run with the World of Darkness storyteller system. And then some anime are best to play in Maid...or not at all.
Conversely though, what if you want to go against the grain? Picture, the Kingdom of Hyrule. The Hero of Time has vanished, Gannon rules the land with a cruel dark hand. A bomb merchant, a Goron guard, a poor desperate farmer, and a magician possessing just a tiny ounce of magic decide to rise up against their wicked king. Their story is one of desperation, of making deals with dark forces and spirits, of battling not just evil, but other people just as desperate as themselves. It's a story of loosing oneself. This game could be played better by something like the song of ice and fire role-playing game, or world of darkness than by a Pathfinder or Savage worlds game.
Because it's ultimately the rules and the intricacies of the system that will reinforce the theme and the emotion of your game they must match up with the feeling and ideas you want to include. So think carefully about what rules set will go best with the fandom or series you want to play in, and when in doubt ask the others at your gaming table about what they want to play and what the core aspects they want to capture are. Hopefully this has been helpful in setting up some truly great games for the future.