Unlike unicorns and honest politicians, they do in fact exist. Unity3D is the leading commercially available high-end engine that does _fantastically_ in this regard. On the hobbyist/low-end, things like GameMaker have been doing this for many years. There are an assortment of other engines around. Do realize that even if you add up all the games using Unreal, Source, CryTek, and idTech, you're still talking about only a teeny tiny little fraction of all the games made so far.
Originally Posted by entropy
Other "AAA-grade" engines exist that do these things, but most are in-house projects and either never licensed out or are done so with very little public fanfare. There are also a very large number of smaller studios with really amazing internal engines and tools that you'll never hear about (which is too bad; some of them really should license their tech).
A lot of smaller indie teams are working with quite capable engines and in-house tools. I know I've said more than a few times here that I had no respect for indie games, but this last year has really seen a huge turnaround. Especially with the very recent trend with Kickstarter and experienced game devs jumping into the indie scene, there's some cool stuff happening that I never would have expected a year ago. Lots of new blood with a solid fundamental understanding of both game programming and general high-quality software engineering are showing up, many migrating from the big companies after the last few years of the big publishers mistreating their developers and artists. I'm still a bit wary of the indie scene (not sure if it's a bubble waiting to pop or an unstoppable force of the market), but they're definitely doing great things, in part by doing their own rapid-cycle game tools rather than using the big-name clunkers.