1. Quick start rules
Never underestimate the humble quick start rules for a system. There are tonnes of them out there and they're all free. If you're looking for a one-shot or even a few sessions, or you don't quite want to commit to a game without trying it first, then quick starts are for you. From Shadowrun to Vampire to Dungeons and Dragons, most creators will have some form of quick start rules to serve as a bare-bones tutorial to new players.
2. Free independent RPGs
There are plenty of full systems out there that you can get your nerdy paws on for absolutely gratis. In fact, I already listed a top 10 free RPGs earlier in the year, so check it out. There's likely something there for everyone's tastes.
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Often gaming stores run their own campaigns or allow you to set up your own game to play. Usually this costs a small fee since, well, they're stores after all, but these games are a great way to play on the cheap and meet some new friends along the way.
4. Create your own
You have to be really creative with this one, but if you have the know-how you can create your own system, simple of complex, and run it with your friends. The best part of this is that you make absolutely everything, so you won't have to buy pointless splatbooks and such. Of course, this may take some time and a hell of a lot of creativity, so good luck!