All proxies I know of run online as a website, however if those sites become blocked they are useless. So I was wandering if it is possible to download a proxy, maybe one that runs as an application.
First I think you need to understand how a proxy works: Think of a proxy as another computer sitting right beside you hooked up to a different internet connection. You want to bounce information from that computer to your computer thus masking your IP address from the target or source.
You can't really 'download' a proxy. Although you can configure your browser to use a proxy (Tools, Internet Options, Connection Settings). You can find some public proxies here, although I'm not convinced that most of the proxies were originally intended for public use.