Archiving Web Pages - Legal or Illegal?

Dyer asks: "I used to run several high-trafficked anonymous surfing sites and if I wasn't getting emailed by a lawyer telling me to block someone's site from being accessed I was being woken up at 2am with a telephone call from a crazy person yelling, sometimes swearing at me with the impression that my site copied theirs and it resided on my server, when in actuality it was being accessed by my server at that instant and being relayed to the user. This is my point, how do services like Archive.org and Google's cache get away with what they're doing? You can call their services whatever you like, but it doesn't change the fact that they are copying people's websites and saving them onto their servers for everyone to access."