I am interested in getting into sound design for games and I'm hearing from most sources that FMod is the way to go. I'm just wondering if you need to have a game designed to use it. I.e. Can I just use it without any game to (currently) apply it to.?
It depends on what you want to do.
With just FMOD Studio, you can build complex events with parameter-driven effects, detailed internal signal routing, randomised elements, and internal trigger logic of a variety of different flavours. You can also mix your project, devise snapshots and sidechains to alter how it behaves under particular circumstances, and audition how things sound together. To put it another way, you can author a game's worth of content without having a game. (Full disclosure: I work for Firelight Technologies, and one of our design goals for Studio was making it possible to design, audition and tweak complex content without needing to dip into game code.)
That said, there are certain things you probably want a game for. For one thing, it's hard to adjust and fit your overall mix to fit the "look and feel" of your game without having said game handy. For another, while Studio lets you control the parameters that drive events as you audition them, it's unlikely you'll be able to exactly mimic the timing and precision found in your game, which is a disadvantage when fine-tuning and tweaking what you've made.
For just learning how the tool works, though, you can get by without a game. That said, FMOD has integrations with a number of well-known and easily obtainable game engines that might be of interest if you ever want to put your sounds into a game.
FMod runs in Unity with a simple to implement Bridge. Then there are basic C# Scripts that you can use to replace the audio in any of the free to download Unity Tutorials. Good luck.