No, ISPs won't normally be doing that. They see your direct access to websites, of course. And unless there's end-to-end encryption, they can see all the information. They also see your connections to VPN services or Tor. But that traffic is encrypted, so they can't see what websites you're accessing. However, your ISP could collaborate with websites or their ISPs to deanonymize your activity via VPN services or Tor, through traffic correlation. And the NSA or whoever could do that with information from them.
