Raspbian is pretty lightweight as far as operating systems go, but if you're looking for something even simpler for your Raspberry Pi projects, Minibian is worth a look.
The current version of Minibian is based on the most recent Rasbian build (Jessie), and is compatible with all the various versions of the Raspberry Pi. This version differs from Raspbian in a number of ways, but the main takeaway is that Minibian is built more for electronics tinkerers than those interested in making a full-fledged computer. Included here are just the core system and some basic utilities (including NAS, web server, and various electronics applications), and does not include a GUI. This makes it great for embedded projects because you get the support and compatibility of Raspbian without the fluff. The end result is a 450MB operating system that can boot in about 15 seconds and only uses 29MB of RAM. You can put it on an SD card the same way you would with Raspbian.
Minibian (Jessie) 2015-11-12 Is Out! [Minibian]