I think I spotted a new breed of games, which I call pseudo-MMO games. Right now they only exist in beta, but I do believe that this could be a growing development. They are made by big game companies, have a sizeable budget and high quality, and play very much like a single-player game. But they are online, Free2Play, and have multiplayer features like the ability to chat or trade with other players online. Biggest example is Age of Empires Online, from Microsoft. Ubisoft has The Settlers Online, currently only in the German version. Firaxis is working on Civilization World, on the Facebook platform.
Traditional single-player games have their problems: They often are hit-or-miss, with a few blockbusters making big money, and many games not being profitable. They often make most of their revenue right at release, while later they don't sell very well, with the business further being eroded by used-game sales and piracy. No wonder the makers of single-player games are jealous of the MMO games, which can be profitable for longer stretches of time. Online account theft is harder than piracy, doesn't generate the same sort of sympathy for the thief as piracy does, and you can even get the customer to pay for measures to protect their accounts, like an authenticator.
A first attempt to get the benefits of MMO games for single-player games was the introduction of downloadable content (DLC). While this will certainly continue, it isn't a 100% success. Often DLC gets chided for being a rip-off, like the famous Oblivion horse armor. And people still manage to pirate the game and DLC in spite of the online account.
So why not make massively multiplayer online games right away? Of course many people do. But making true MMO games isn't quite as easy. And some genres, like strategy games, have serious design issues with being massively multiplayer: In typical browser MMO strategy games players often end up being ganged up upon, and attacked during periods where they are offline. There is a market for that sort of game, but don't expect people to spend too much money on building up an empire that is going to be destroyed by jealous neighbors. So browser MMO strategy games are usually low-budget affairs, with minimal customer support, run by small companies specialized in that sort of game.
But now big game companies have learned some tricks from modern MMORPGs: Using tricks like instancing and phasing, you can create a single-player experience in a massively multi-player game. And that has led to the development of the pseudo-MMO games. While being online strategy games, large parts of these games are PvE. The central part of the empire the players are building is completely protected from attacks by other players, PvP only happens in battleground-like instances. Thus players are willing to invest money into building up and decorating their empire. So these games can run on a Free2Play business model, attracting lots of players for being "free", and then enticing them to spend money.
While there are certainly influences and features in these pseudo-MMO games which will remind you of Facebook games, these are actually high quality strategy games with real gameplay made by established big game studios. And they are true online games, impossible to just pirate by copying or hacking some DLC access code. While their multiplayer components aren't strong, they do have chat and the possibility to trade resources among players, as well as the ability to show off your empire to your online friends. They combine many of the best features of browser strategy games with the best features of single-player games, while avoiding most of the pitfalls of their parents.
While this is still early days, I do think that these kind of games have a bright future. With a few exceptions like Starcraft 2, the strategy game genre isn't doing all that well at the moment, and could profit very much from a move towards online, like RPGs did. I wouldn't be surprised if many of the classic strategy game series will revive online in the coming years.