My number one choice for ease of use is: Twitter Gallery - Pick a free twitter theme by category or color and then have it automatically installed on Twitter. Ten minutes, max.
Use a visual designer with more options: PrettyTweet - Use the on site WYSIWYG editor to design your free Twitter theme. Add, crop and adjust image, change border, link or text color. Post theme automatically to Twitter and have background image emailed to you. Twenty or more minutes.
cheth Studios - Free background pictures (PSD format) from DeviantArt.
FreeTwitter Designer - Create free Twitter backgrounds using an on site tool.
SweetTweet - Cute, fun free backgrounds organized by categories.
TwitterImage - Free Twitter background pictures by category.