LMMS - Make music with a free, cross-platform tool
Ardour - Record, edit, and mix on Linux, Mac OS X, and Windows.
Reaper - Reaper is a focused digital audio workstation (DAW) developed by Cockos. In the creation of the software, the digital audio technology company intended to make audio editing accessible to the masses.
GarageBand - GarageBand is a fully equipped music creation studio for Mac
Audacity - Audacity is a free and open-source audio production software suite that includes a surprising array of editing tools and recording systems.
FL Studio - Image-Line's FL Studio, now on it's 12th version, is a well-known music production suite and the most popular beat processor on the market, due no doubt to its longevity. Read more about FL Studio.