Here are some of the ways that I have played with using greeting cards as craft supplies. Sometimes I recycle cards and sometimes I use new ones. You can click on the picture to visit the blog page about that project.
Three sided wraps
Double Ball Ornaments
Ornaments with "fins"
Double hearts (and ribbon trees)
These card balls are usually done with greeting cards but I used used heavy paper instead.
Here are some projects that I would like to try using greeting cards. (If you click on the picture you will be taken to the page where I found the project.)
Woven stars and snowflakes
Seven circle ornament