Probably the most common open tunings is open D.  It's used in all kinds of music...blues, rock country etc. It's called open D because when you play all the unfretted strings you get a D major chord.  Low to high the guitar is tuned D,A,D,F#,A,D

 Here's a V chord or G in open D.

You can also play a G by laying your finger straight accross the 7th fret.

A IV chord or A in open D.

You can also play an A by laying your finger straight accross the 5th fret.

and your I chord or D. 

You can also play a 1 by laying your finger straight accross the 12th fret.

With these three chords you could play any number of blues tunes...

A great tune to begin with is Amazing Grace. You can play it with just the chords above.

There are tons of Open tunings to explore, and many playing techniques to compliment them. Many players use open tunings for slide playing, and lotes of fingerstyle is done this way also. one of the first tunes I learned with open D was the Alman Brothers, Little Martha.

http://www.musiclessons.com/youtube/share.cfm?v=-FXHdiOX9Rw&t=Little%20Martha%2FAllman%20Brothers%20(tutorial)%20-%20cover%20by%20Tonedr

I've always been a big fan of the DADGAD tuning. Here's a pretty good article about it:

http://truefire.com/blog/guitar-lessons/secrets-dadgad-open-tuning/

This is a great lesson...It's About Open D, and it's just a bunch of ideas for what you can do with it rather than a specific song. 

https://www.musiclessons.com/youtube/share/?v=klPbAN-1Yo8