Google Site Search, a service previously known as Custom Search Business Edition, falls in the same category. Google offers a hosted alternative for small businesses that want a powerful site search, but don't need all the features offered by Google's expensive search appliances, which are mostly useful for intranet search. Google Site Search is based on the Custom Search platform, but is fully customizable through XML feeds, includes support and doesn't have ads (they're actually optional).
One of the major problems with Google Custom Search was that it used the same index as Google's web search engine, so the site search was just a restriction of Google's web search results. Google realized that people were unhappy with these limitations and decided to create a separate Custom Search index. "We're now maintaining a CSE-specific index in addition to the Google.com index for enhancing the performance of search on your site. If you submit a Sitemap, it's likely that we will crawl those pages and include them in the additional index we build."
The most important new feature offered by Google Site Search is an enhanced indexing, but Google is quick to mention that this doesn't affect Google's main index. "Any additional pages in the Google Site Search index aren't included in Google's index and won't impact a site's behavior in the Google search results."
The other 3 additions to Google Site Search offer simple ways to influence search results. You can upload a dictionary of synonymous to improve Google's query expansion, it's also possible to give more weight to recent web pages or to pages from a specific section.
Unlike many of its competitors, Google Site Search still can't index password-protected pages and it doesn't let you decide how often to index your site's pages, but the price is hard to beat: starting from $100/year for 5,000 documents.
If you don't need support or advanced customization, Google Custom Search is still free. There's also a competition for winning a subscription to Site Search and Google T-Shirts: the only condition is to submit the address of a site that doesn't have search features (quickly remove the search box!).