Here are all the giveaways I could find from various print on demand services and POD shops (whether they're sponsored by the POD or by individual artists who work through them.) If you know of any others, please let me know!
Artist/Shopkeeper/Blogger Sponsored Giveaways
These giveaways are sponsored by artists who work through PODS. They are usually for specific items from the artist's shop.
Set of 5 x 7 Pretty Poison Prints by Elvenstar Art (7/12) - Possibly Zazzle
POD Sponsored Giveaways
The following giveaways are sponsored by various print on demand services.
Spoonflower Fabric and Collete Pattern (7/9)
$50 Zazzle Giftcard at the Mommyhood Chronicles ( 7/10)
CafePress Gremlins Bag (7/11)