@brahmin,
It seems like you are looking for
data warehouses more than
data mining. And it seems like you are focused on the web mining, which really makes it a bit meaningless since
any large internet company does those things and depends on traffic analysis (a form of data mining) for their success.
So just pick any large internet company. Yahoo and Microsoft both operate large-scale search engines like Google. In Yahoo's case it's a significant part of their revenue and the search engine is their most valuable asset. I also mentioned Technorati, which does the same kind of web scraping that Google does to provide a blog search and blog rankings.
Shopping comparison sites like PriceGrabber, mySimon, and NexTag all mine the web to aggregate and analyze products for their customers to search.
Just about any company uses data mining in some form, but it looks like you are focused on customer-facing products of data mining like search engines and e-commerce sites. You can really just pick any you know, and find ways they are doing data mining (any "recommended products" or "best sellers" list is an example, and if they have any traffic worth speaking of they are using web analytics software extensively to mine data from it).