Gorgon Zee
Hero
Basic Roleplaying (Chaosium) can, and it is definitely in the camp of providing many, many options for you to choose from. It’s much like GURPS in that respect, but I find it cleaner and much more consistent. The single volume currently available which contains specific systems for all the above genres is a strong choice. As I’ve stated before, I’m not a big fan of the style, but it would be my go to if I Wally wanted to mix up multiple genres in a medium-crunch system.Are there generic systems that can do fantasy, sci-fi, horror, modern, etc all in one?
Fate also works for all of these — I’ve run sci-fi, horror and modern campaigns using it. It has a different approach — it provides a light engine that you need all of, but you will also need about 50% more content in the form of a world book or the like for a specific genre. I like that style — no waste and minimal useless extra stuff, but it does make Fate more of an engine than a system.
Powered by the Apocalypse is another generic engine that has multiple incarnations that tailor a generic system. I’m not a huge fan, but many are and there are a lot of very highly regarded options in each of these genres.
Savage Worlds I used to run a Flash Gordon campaign with minimal changes, and it’s good for a game with a pulp feel. But when I ran a more recent Deadlands campaign, I went back to the original system as although a worse system as a rule system, it was way more that if and fit the genre better.
I’ve run Alternity and Cypher system campaigns also, but spite them being marketed as generic, they had a very strong way of working that affected the games I ran, so I’d hesitate to call them truly generic. More like the d20 modern games that alway felt a compromise.
So .. any of the above could do all those genres, but each has their own drawbacks and will bend your game to their way of running. If that’s to your liking, fantastic! For me, it’s been easier to find a smaller, focused game than work out which behemoth to use and then spend the time trimming the fat.