Indices are useful if you are simply browsing, but often you have a particular topic in mind. In that case a searchable index is preferable. Some of the indices on the NCSA MetaIndex are searchable, most notably the W3 Catalog maintained at the Centre Universitaire d'Informatique, University of Geneva. A weakness of many of the searchable indices is that they are based on the titles of documents and not on contents. There are now many sites that maintain databases that index the contents of pages on the web. I mainly use Altavista, a service of Digital Equipment Corporation, but there are several others including Web Crawler which was developed at UW, and is now maintained by AOL, Lycos, Infoseek, and Excite.
What are some applications of the web? Here are some examples I particularly like. What if all journal papers were available on the Internet? Here's one example of how one would look. And some others. As oceanography matures, observations are increasingly being made with arrays of in situ sensors. At present, much of this information is stored and retrieved when the instrument is recovered, but eventually this data will be telemetered and be available on the Internet. There are already some examples, like the REINAS Project being conducted around Monterey Bay, California and through the server maintained at the Center for Coastal Studies at Scripps. (Atmospheric sciences already take full advantage of these capabilities. What's the weather? Seattle Traffic has been on-line for about a year.) The web makes using large data sets much simpler. For example, one component of the RIDGE program is to make the data describing the topography of the mid-ocean ridge readily accessible. The "forms" capability of the web is being increasingly used as an interface to computer-based models. Here's an example involving motion of the Earth's plates.