While I was searching for information about the Tesseract for this question, I read something I forgot about the Captain America: The First Avenger movie in the Cosmic Cube wikipedia article:
During World War II, Johann Schmidt captures the cube in Tønsberg, Norway, claiming that it is "the jewel of Odin's treasure room".
Why did Odin leave something as powerful as the Tesseract, one of the most powerful artifacts in the universe, in a relatively unprotected treasure room in a remote world like Earth? Why didn't he take it back to Asgard where he could keep an eye on it?