Once upon a time, when computers were still beige boxes that ran pretty slow, all strategy and role-playing games were turn-based. That wasn't so much a design decision, but rather based on the limitations of the platform. As soon as computers became powerful enough to run real-time combat, nearly all strategy games and many role-playing games switched to real-time. Which is a pitty, because often the turn-based games were better and had more depth. Is turn-based gaming heading into history's bin of oblivion?
Turn-based gaming is alive and well on platforms where technical limitations still prevent a move to full real-time combat, for example hand-held consoles. You'll find relatively more turn-based games on hand-helds than on full-size consoles. But with hand-helds like a PSP being already nearly as powerful as a PS2, that limitations is falling. Me buying Tales of Eternia and expecting turn-based combat, but then getting a real-time combat game I didn't like is a good example. Strategy games on hand-helds might be stuck in turn-based for a while, because of the size of the screen. It isn't easy to run real-time strategy on a tiny screen without losing overview.
Another unexpected corner where turn-based combat is still thriving is MMORPGs. Game companies did a good job of disguising it, but at the heart of it a game like World of Warcraft has turn-based combat. There are pseudo-turns, given by the rhythm of the automatic attacks, leaving you generous amounts of time to perform special attacks. Again the reason for this is a technical limitation, the speed of the internet. The timescale of combat is given by the latency of the players, which limits it to tenths of seconds, not milliseconds. And that will be hard to fundamentally change unless the internet changes fundamentally. People will complain if they lose combat because their ping is slightly higher. In Final Fantasy XI there was a controversy once, where American players felt disadvantaged when trying to "tag" named monsters, because Japanese players being closer to the servers always beat them before they even say the named mob spawn.
In single-player games for the PC or next-generation consoles it is getting hard to find major games that are turn-based. Besides Heroes of Might and Magic 5 I can't think of any recent triple-A PC games that are turn-based. But the PC has a big advantage here, a big independant games scene. Indie games are technologically less advanced, plus they cater to audiences that the major game companies consider "niche". So there are lots of indie turn-based games for the PC. No such luck for consoles, due to the proprietary nature of these there are no indie games for them, and thus less and less turn-based games.
So we can only hope that major game companies rediscover the advantages of turn-based games. While real-time combat looks more realistic, turn-based combat is closer to the experience of board games or pen & paper role-playing. By making combat fast, it loses a lot of depth, making fast decisions more important than good tactics. But the gaming population is getting older, and thus less interested in shallow, fast action. Older player like to be challenged intellectually, to think while playing. Not just because they are slower than the teenies, but also because the aren't so easily pleased with flashy graphics and special effects hiding a shallow game. Turn-based franchises like Civilization or HOMM keep selling very well, so there would be room for some new brands in this field. Just because you *can* make combat real-time doesn't mean that this is the best option for strategy and role-playing games.