As Debian big fan, sometime I found that apt-get update command reveal this error:
“E: Some index files failed to download. They have been ignored, or old ones used instead.”

This command is very simple solution I found:

# rm /var/lib/apt/lists/partial/*

After that, apt-get update && apt-get upgrade command should be fine.

Source:
– http://forums.debian.net/viewtopic.php?f=10&t=108618