Accessing GPS data with JavaScript in real time

Yes. You are looking for the Geolocation API, here's a simple demo. Here is sample code from Dive Into HTML5 and HTML Rocks. Works great from web pages hosted on iOS and Android phones, it's a simple API to use. Strictly speaking it's not GPS; it's a generic location API. On mobile devices like iPhones location is often provided by WiFi or cell tower fixes and not the GPS radio.

I've used solution, where Java applet was reading NMEA GPS data from serial port and wrote it to browser's global variable - where it was accessible to JavaScript. It worked well on laptop and regular browser, not sure, how it would work on smartphone.