My requirement is to write an application which is GUI based has to run on browsers. Could you tell me which one would be suitable for this?
These are generally 2 different things: either you're writing a local GUI rich-client (in which case, use the GuiProgramming wiki link Mike sent), or you're doing web development targeting browsers in which case you should investigate the myriad web programming frameworks for Python (Django, Turbogears, CheryPy, web.py, webstack, etc).
There's a third "type" of application that I abhor, usually developed in Flash/Silverblight/JavaFX that runs within a web-browser, but allows for richer interactions/rendering than your average web-page. However, I don't know of any python tie-ins for any of these environments.
There's also a blurred line if you embed a web-browser in a local GUI application.
-tkc -- http://mail.python.org/mailman/listinfo/python-list
