Stephen Wolfram and his folks have silently started an amazing thing:
WolframCloud.COM (click!)See also Wolfram's blog post, Wolfram Programming Cloud is live, that offers you some cool examples what you may do right now.
I came to the web above, WolframCloud.COM, and tried a username/password combination I used to use with some Wolfram Alpha widgets or something. It has worked! You may create a new account over there, I guess.
What's really new and live on WolframCloud.COM is the "Wolfram Programming Cloud". You may click at many things over there, including "New". The latter gives you a Mathematica (more precisely: Wolfram Language) notebook interface of a sort. But everything is run on Wolfram's computers.
Lots of the functionalities you may expect from the cloud will satisfy you.
You may try to type 2+3. The characters aren't aligned properly on my monitor but it's OK. As a genuine Wolfram beginner, don't forget to press shift+enter to evaluate what you wrote.
You may also press ctrl+= for some Wolfram Alpha-like, natural-language-based conversation with the system.
I am not sure yet how far you may get with a free account but maybe, you get very far and it may be an excellent reason to try to learn the Mathematica/Wolfram language a little bit.
I've tried some semi-simple code I had in Mathematica. Up to the misaligned layout and the need to copy-and-paste the commands separately, it just works and produces the graphs and images I am used to from Mathematica on my laptop. I've uploaded (the arrow-button next to "new") a whole 2012 notebook drawing Penrose tilings and it works, too.
If you have nothing else to try, you should check the Penrose tilings, too. Download this Penrose tiling code of mine to your PC. Create an account at the Wolfram Programming Cloud. Upload the *.nb file you just downloaded to the cloud. And shift/enter go through the commands of the file to check that they're recalculated properly and the resulting Penrose tiles are regenerated in the Cloud.
One needs to emphasize that this is not just Mathematica. As programmers will understand, you may "deploy" the things, run them as APIs, and so on.
Congratulations, Dr Wolfram et al.!