Economic Principals has an article summarizing some of the successes of Auction theory over the last few decades. They highlight its role in the privatization of Eastern European government assets, the FCC wireless spectrum auction, and even eBay.
Read the whole thing Here.
Although not mentioned in the article, auctions have also made significant inroads in finance. Dutch auctions have been used for years in stock repurchases, and auctions are even being used (albeit infrequently) for issuing stock in an IPO.