Fully Battened Sail
This is David Sargent's sail, it is a cut down Hobie 16 main sail. The sail uses the battens to stiffen the sail and help hold it's airfoil shape. This also has a gaff on top.
Chinese Junk Rig
This is probably the most recognizable batten type sail, and for those that like them, they usually fall deep in love with them. The junk has many battens and on some configurations, each of the battens has it's own control line.
This one has the luff of the sail attached to the mast, but I have also seen junk sails that have loops in the battens, so the sail is attached just aft of the luff a bit.
Instead of being shaped with draft like a typical sail, each panel is just a simple flat shape and the theory is they create lift by the way the panels vibrate.
This duck has a jib sail, but typically junk sails are used without a jib.
One of the problems with triangle sails is the top part doesn't seem to be doing much work other than holding up the rest of the sail. One technique to add more area to a triangle sail, is to add a square head to it. This one has a special mast that has an L shape on the top to hold the top of the sail. Most common is to have some battens in the sail to hold it open.
Square Head w/Leech Battens
This is another technique for making a square head, a sprit is added to hold the upper corner. Also this sail has short battens built into the leech to give the sail more area. Without the battens, the extra sail area would flutter and ruin the laminar flow.
Here is another trick for adding more area to a triangle sail, the clew has a club (stick). This gives more sail area without the complication of battens or an extra sprit.