You can watch a whole episode of 交響詩篇エウレカセブン（Eureka Seven） for free till April 23 at the membership distributor's site:
Show Time (licensed distributor)
Find out the title in the list and click on it, or just click the picture on the right.
It is said that Eureka Seven could be one of the best anime series for this Spring among the anime fans in Japan.
