First, the short version: stop looking for “free”.
Now, in more detail: you're looking to consume some somewhat-non-trivial computing, data storage and networking resources. Presumably you've got a good reason for doing this; if you truly have, you'll have the ability to also purchase the resources required for what you want to do. There are a few options on this front, none of which are free:
- Buy and host your own hardware.
- Buy the hardware and host it in a colocation facility.
- Hire the hardware
- Long term hire
- Short term hire
All the Amazon are doing is short-term, easy set up hiring of resources. Their prices are quite keen (if some other option is cheaper, it's because it is missing something significant that Amazon do; maybe it's something you don't need but that's up to you to figure out). You can host the core of the Amazon API quite easily on whatever resources you've hired (see Eucalyptus) but be aware that going from having the software and the API to having everything work smoothly is a really big step; the more I work with Eucalyptus installations, the more impressed with Amazon I become. And that's despite being also pretty impressed with Eucalyptus itself.
But none of this is free. It takes real resources to provide – e.g., electricity to power the machines and keep them cool and a building to house them in – and ultimately, that's got to be paid for somewhere. To expect otherwise is to believe that others should have to pay for things for you; it's pretty rare that that happens, and the more you need to consume, the rarer it is (especially if the economy isn't doing too good). So stop thinking in terms of how you can get it for nothing (“freeload”) and instead take a good look at what it really costs to provide through various routes and seek to minimize your costs. If you can't afford even that, your #1 problem isn't hosting but funding; fix that first.
Rest assured you're not alone in this matter. This is what lots of other people worldwide have to do to make their projects into reality. Good luck!