opc.net is offering a free remote LXDE desktop on which you can run various applications (like Firefox, Chrome etc.) for 1 month.
Free account is very limited and restrict you with 200mb of storage. No root of course.
A good thing is the super fast and easy registration: From the moment you decide to register it will take only 2 minutes until you access your remote desktop (desktop will appear right on your browser).
You can use it to experience and play with LXDE desktop, or as a proxy to surf internet.
Applications for smartphones available.
I have not tested this service enough and probably missed some points. Feel free to add details
