Monopoly #1 is in online auctions. EBay owns the market, and no competitor has ever been able to even become a blip on eBay's radar. It's a textbook example of the power of the network effect. Despite having had a disaster of a CEO in Meg Whitman and a so-so CEO in John Donahoe, eBay has a very wide moat in online auctions, and that won't change for the foreseeable future. Even the privately held Craigslist, which is a competitor in the "Time-To-Clean-Out-My-Closet-And-Sell-This-Junk-Online" market, is about a quarter-owned by eBay, so they get a piece of that action too.
Monopoly #2 is PayPal. If you're a small company or entrepreneur doing business online, it can be prohibitively expensive and complicated to get a merchant account, plus having the merchant account won't enable you to do business globally and in several currencies. But PayPal solves all of that for you. Plus PayPal has the aforementioned network effect, in which case no competitor can hope to ever match its user base, which creates a moat. PayPal gets a little piece of the action all over the world in ecommerce.
Since eBay charges auction fees and PayPal fees *mostly* as a percentage, this gives it built-in inflation protection that is better than 90% of the other businesses out there have.
In conclusion, eBay has an extremely solid business model. Although its R&D and SG&A expenses are a bit high, and its CEOs have been way too feverish about over-paying for acquisitions with the shareholders' cash, it's the power of its business model that is making eBay a winner in the long run.