Last school year I decided to start teaching guitar to my music tech students because I wanted to help them hear chord progressions and changes.  You see, we had been making songs in Garageband using the loops and layering bass and guitar and keyboard loops together, but if the loops had incompatible chord changes, the resulting song was a mishmash of harmony.  I wanted to help my students understand how to put Garageband loops together and to listen for the chord changes in the loops by having hem actually play chords.  Guitar was the perfect instrument

The first semester's goal was simple: learn three chords (G, C, and D).  Since I was a beginning guitar player, I wasn't able to teach my students very much.  Luckily, they were beginners too and we got along just fine on three chords for a semester.

In the second semester last year I was blessed to have a student who was a natural guitar player. He taught me some of the "tricks" of playing guitar and changing from one chord to another.

This year, I am blessed with four really good guitar players who took Music Tech just to play guitar! There are three other students who are beginning players, so I adopted an aerobics mentality to teaching the chords this year: low impact (simplified chords), middle impact (G, C & D), and high impact (added minor and 7th chords) 

Here's just one of many sites that lists songs that can be played with just three chords on the guitar.

http://www.4shelties.com/banjos/3chrdsongs.htm