Sun Conure
The Sun Conure Pattern is free.
The sun conure has a jointed neck and wings. Someday I'll put stronger wire in his feet so he can hang onto things by himself.
All images copyright Silver Seams.
Other Interpretations
Cat of Raggyrat made a puppet (two, actually):

(As you'll notice, she scaled the pattern up a smidge....) There are some more pictures in Raggyrat's photostream on Flickr, and
work-in-progress entries in her blog.
Amanda of Corsetra's sewing diary made a jenday conure (with an eyepatch and pirate hat, too).
As always, I'd love to see pictures of finished (or hey, in-progress) items, especially if I can post them here (or link to your page of pictures, whichever). And if you're selling them, or if you can be commissioned to make one, do let me know and I'll link to that, too.