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This is an ever-changing list of the ring exercises and stretches I perform in my routines. Gathered from various sources, they require only a pair of rings and are great as an accompaniment to (not a replacement for) weight training.
Atomic Push Up
Bulgarian Ring Dips
DIY Hanging Handles, psuedo "rings"
Foot-Ring Push-up
How to Perform Ring Push Ups
Larry Scott performing Ring Flyes
Muscle-up tutorial on Beast Skills
One-arm Ring Push-ups
One-legged Divebomber Push-up
Ring Dips with Progressions
Ring Pushups demonstration
Skill Transfer for the Muscle-Up
Sonnon's Lawnmower Extension
The Ice Cream Maker
Upside Down
You might also like to look at the exercises using bands, kettlebells, plates or the main exercise index.