No, they won't spam you. If you think They have put a tiny device in your keyboard that records everything you type and sends it to the Illuminati satellites so the Greys can keep tabs on your every action, you may be right. Well, except for the Illuminati satellite part. Key loggers are programs that record every keystroke made by the user. Any reasonably expert user can set up a logger to output to a hidden file, or a file on a network drive.
Some loggers can send their output to a distant machine over the Internet.
Loggers are simple enough things, in essence. The only subtlety in them lies in making them as undetectable and unkillable as possible, so users don't know they're there, and can't turn them off even if they do. Key loggers have also evolved into more advanced products that monitor what people click on and pretty much everything else they do with their computer. There are some people who have good reason to use key loggers. Financial institutions and military organisations, for instance.