Currently the most popular web browsers are Mozilla Firefox, Google Chrome, Microsoft Internet Explorer, Opera and Apple Safari.
Initially, JS was just used for simple interactions with the user (e.g. displaying prompts, verifying forms before submission to the server etc.). At this stage, execution time was not really an important point, but with increasing reliance on JS, many advances have been made to improve it. The staggering improvement in speed is only just being realised by coders, with some amazing projects currently being developed. Some of these include a pure JS H.264 decoder (allowing H.264 videos to be decoded in real-time at 30 fps), a JS JVM (a Java Virtual Machine, allowing Java application compiled to byte-code to be executed) and even a full x86 system emulator that is currently capable of running Linux and Windows with persistent storage inside a browser using HTML5.
The incredible power of computers these days means that things like this are now possible and browser developers are keen to be at the top performance-wise. Google is obviously seeing the potentials with the introduction of their brand-new scripting language "Go". It will be interesting to see how far this technology has reached in one year's time.