"Mozilla and Unity are announcing new deployment tools bringing Unity-authored games to the Web without the need for plugins, made possible thanks to Mozilla-pioneered technologies including WebGL, a Web graphics library and asm.js, a supercharged subset of JavaScript. Unity’s WebGL add-on will be made available with the release of Unity 5.0 later this year."

Using open web technology such as WebGL and asm.js it should be pretty easy for developers to port their games to the web using the upcoming version of Unity. Currently Unity web games require a browser plugin and after the new version is out developers can start building native browser games.

Now that Internet Explorer is supporting WebGL if things works well enough, native Unity games "should" work everywhere.

https://blog.mozilla.org/blog/2014/03/18/mozilla-and-unity-bring-unity-game-engine-to-webgl/