Fair use says that some uses are legal even though they’re not explicitly allowed. Backups of material you are already licensed to are covered by fair use, even if (for instance) a piece of software’s EULA says otherwise. I’m pretty sure email delivery falls under this as well.

Unfortunately it’s not very well spelled-out, but you should be aware of your rights under fair use as they supercede regular copyright restrictions in many cases: http://en.wikipedia.org/wiki/Fair_use

Luckily, people aren’t THAT dumb. They are close to that dumb, but not quit. The reason it doesn’t really come up is that if there is a case of infringement on a computer, the people sue for the unlawful replication that they can prove; like the song on your harddisk. I believe, but have no basis for, that if the suing entity then told the judge they wanted to multiply the damages by 6 because the infringer’s computer made a copy in memory 6 times because that is how many times they played it, the judge _probably_ wouldn’t let that fly.

Also, ISPs are considered a “safe harbor” under the DMCA; check out the Chilling Effects website FAQ: http://www.chillingeffects.org/dmca512/faq.cgi