And then there are sites that offer unique functions that don't fall into any of these categories. One advantage of hierarchical indices is that the pages that are included have been evaluated and categorized by trained persons. On the other hand, the need for human intervention in the indexing process limits the number of pages that can be included, compared with the automated search sites. If you have a relatively general search, an hierarchical index site will will likely return fewer pages, but the pages will likely be more relevant. If you instead want to find everything you can on a very obscure topic, the sites with automated search agents will probably get you more hits.
Many sites have both directory and search capabilities.
I've listed the search sites that I know of below. I haven't tried to arrange the sites into functional categories, but instead have taken the easy way out and have just listed them alphabetically. AlphaSearch is a directory of web resources pages, full text documents and on-line databases relating to academic fields. Browse by academic category or search by specific terms. Boolean search available.