I keep getting hits from people searching for free amigurumi patterns. They get directed to my Japanese Craft Books post, which does not include the free patterns those searchers are looking for. So here you go! This post will be updated periodically with more patterns!
CROCHET
Sprite, by Even Howard, was published by Crochet Me magazine.
Fairy Tales at Your Fingertips finger puppets, by Melissa Mall, Crochet Me August/September 2005
Autumn's Apple finger puppet by Kat Marie Williams, Crochet Me Oct/Nov 2005
Cheeky the Octopus by Melinda Fisher, Crochet Me Oct/Nov 2005. Melinda also sells some of her crocheted toys through her mintimindi Etsy shop.
Crocheted stegosaurus pattern by Knittykat, available as a .pdf download for free, with a request to make a donation to a specific charity.
Moldy Cupcake from Gleeful Things (more patterns are available for sale).
The Amigurumi-Along has links to free and not-free patterns and loads of photos of all kinds of amigurumi. A frequent poster there is Roxycraft - her site has free patterns (but not amigurumi patterns). She sells her amigurumi patterns as PDF downloads, and also sells the finished amigurumi. Her patterns are super-duper cute and well worth the money! You can also check out Etsy shops for finished amigurumi as well as patterns by indie crafters.
Craftster.org has free patterns and links to free patterns in the forums, like the penguin by tamar, and the panda and pig by mmmfruit. A search for "amigurumi" in the forums will result in several pages of hits.
Crochet me has an Amigurumi Special Issue! Includes patterns, tutorials, and how to make your own variations on a basic pattern.
Designer Ana Paula Rimoli has a blog just for her free patterns: Free Amigurumi Crochet Patterns:
Little Cookie
Little Bunny Rabbit
Pablito the Penguin
Cat & Mouse
Zequi the Bear
Cupcake
Little Fried Egg
Ana Paula Rimoli also sells patterns and finished amigurumi through her Etsy shop, www.anapaulaoli.etsy.com. I've purchased a few of her patterns and they are well-written and easy to follow!
There's a new free online knit and crochet magazine, For the Love of Yarn. The premiere issue has crochet amigurumi patterns for a turtle and a snail.
KNIT
Don't crochet? There are several free knitting patterns for cute stuffies and toys!
[UPDATE 2009: MagKnits shut down in April 2008; many of the patterns published have been made available by the designers in various locations. I have updated the MagKnits patterns listed below with new links; a couple of them go to Ravelry.com pages and you will need to be a Ravelry member - sorry about that, but the designers chose to host the patterns on Ravelry, and Ravelry memberships are free.]
Gattino, a kitten stuffie (Knitty Fall '02)
Finger Puppers (Knitty Summer '03)
Pasha the Penguin (Knitty Winter '04)
Bubby the Bear (Knitty Fall '05)
Pumpkins (Knitty Fall '05)
Garden Variety veggie toys (MagKnits Sept. '05) [link to Ravelry.com page]
Pocket Creatures (Knitty Winter '05)
Kate, the cat with britches (Knitty Winter '05)
Sushi (MagKnits Feb. '06) [link to Ravelry.com page]
Noblin Breakfast Bunny (MagKnits April '06) [link to designer's page]
Laura Jane Bears (MagKnits May '06) [pattern currently unavailable]
Norberta the Dragon (Knitty Winter '06)
Nautie the Nautilus (Knitty Spring '06)
Sheldon the Turtle (Knitty Winter '06)
Dad's Blueberry Pie (MagKnits Nov. '06) [link to designer's page]
Woodins (Knitty Fall '07) - little woodland creatures and their log home.
The Crochet and Knitting Diva has list of free patterns and amigurumi blogs, some of which are also listed in this post.