You may be able to run Unreal Engine 3 in your browser right this moment, with no installation. Epic Games and Mozilla have collaborated on a native port of the engine's Citadel tech demo to JavaScript, OpenGL, and HTML5.
You can find the the demo right here; keep in mind you'll likely need Firefox's nightly build to run it. Feel free to try playing elsewhere, but it crashed when we used Chrome.
Most browser games require some extra finaggling with plugins or add-ons, and some even launch a separate program. Citadel doesn't have the visual firepower of the Infiltrator Unreal Engine 4 demo, but it gives us a lot of hope for the future of easy, accessible, browser-native gaming.
The video below shows HTML5 Citadel if you can't get it to load, as well as some browser-based Unreal Tournament III gameplay.