Audacity, which is open source, is the first stop on any producer's list of free beat-making tools. Many top producers even choose it over programs costing hundreds of dollars for its simple recording and mixing engine and host of plug-ins. Audacity doesn't deal with MIDI at all, though. It is a raw sound-producing, editing and mastering engine only, so you'll still need something else in your free beat-making tool kit.
HammerHead is perhaps the most simple drum sequencing software on the market, and best of all it's free. HammerHead allows you to create complex drum beats with a simple drag-and-drop interface using the provided drum samples. There are only a few included drum samples to play with, but it's free. HammerHead is an easy-to-learn free beat-making tool and can definitely turn out original, professional sounding drum beats if you know how to tweak them a bit after the fact.
Another great free tool that is especially useful when working with small samples is Expstudio's Audio Editor. When working with free synths and drum and bass track generators, a program such as Audio Editor is useful to mash up, distort and experiment with the samples to make them your own. That's how your finished beat, which you create in a free program like HammerHead, doesn't sound like something canned. This program excels at processing small samples, and best of all the differences between the free version and the professional pay version are slight.
REAPER, with an unlimited free demonstration period to try its features out, belongs on this list of free beat-making tools even if it is technically a $50 shareware product. If you find yourself using it frequently making and sequencing beats, you really should pay the fee as this program has been updated tirelessly for years by a single individual. There's lots to like with REAPER, specifically its ability to host VST plug-ins, which will seriously open up your horizons in the beat-making tools available to you. Free VST plug-ins are available all over the Web.
Without a full-featured beat-making suite such as Live, Acid or FL Studio, would-be producers looking for free products will have to resort to using some technical ingenuity when approaching making beats for free. For example, you can make a drum track with the most basic of sounds in HammerHead and then export it into Audacity or Expstudio before adding extra layers with a software synth VST plug-in in REAPER.
At some point, all this shuffling and composing parts of your beats in different free beat-making tools ceases to pay off, especially if you are getting serious about production. Ultimately, it pays to invest in one of the many excellent audio production software suites on the market. Until that time comes, have fun with these freebies!