Called the Google Custom Search Business Edition, this is a hosted site search, designed for small businesses with web site content, who don't want the advertising displayed on the older Custom Search Engine.
This version uses Google's existing index of the Internet, searching all the pages they know about it on the specified sites including non-HTML file types, using their query language, retrieval and relevance algorithsm, and searching in multiple languages and character sets. Like the web search engine, there is no way to index pages protected by access control such as passwords or ACLs.
The default interface customization is limited to a logo and colors of the results page border, title, background, text and links, but the XML results format is fairly configurable using the Google AJAX Search API. While there is no structure in place to display site advertising on search results, presumably one could do that very easily with XML results. Reports are limited to top queries and queries per day/week/month/all, but can be connected to the Google Activity Monitor site traffic analysis tool.
Note that Google will not guarantee that they'll crawl all of the pages of a particular site, update on-demand, or even update frequently. Using this service will not improve a site's position in the Google.com search results.
Pricing is $100 per year for up to 5,000 pages; $500 per year for up to 50,000 pages (both payable by credit card via Google Checkout). According to ecommerce-guide.com, it seems to go to a $15,000 per year fee for up to 1 million pages, but potential customers should contact the company. (Non-profits, university and government agencies can use the standard Custom Search and opt-out of advertising).