A new generation of programs, offline browsers, can help you by monitoring your favourite sites and checking them for updates at times to suit you -- and your phone bill. When you next check in, any updated pages will have been downloaded and will be available on your hard drive for you to peruse at your leisure.
Most such programs allow you to select a list of interesting sites to monitor (yes, you still have to browse online to find the sites, although some programs provide a preset list). Some will also allow you to download only the text from pages, to save time when checking in at graphics-intensive sites.
Offline browsers are still in their infancy, and as such tend to be available for only the more popular platforms and browsers; most tend to work with Netscape on a PC, although the scope is broadening as the market grows and becomes more mature.
Another way of finding out when your favourite sites have changed is to run a notifier in the background. These programs run while you are online, and scan your favourite sites; they can either alert you to changes and let you decide whether you wish to see the new page, or download it automatically. They won't log on in the middle of the night, but they will let you check whether your preferred pages have changed before you waste time downloading them again.
Because notifiers have been about for longer than offline browsers, the programs (or, in some cases, services) tend to be more stable and reliable.
Some of the online browsers to watch out for are Freeloader, Smart Bookmarks and Surfbot. Notifier names include Netbuddy and the unexcitingly-named Web Page Update Notifier, which is included on the Internet Mania CD from Corel.
Freeloader (still in beta test [March 1996]):