The Market is not the only place you can find applications for your Android device. There are sites who have downloads to a specific genre of apps. Others like Appbrain are aggregation sites. They pull apps from all over the web, not just the Android Market.
The neat part about Android app sites, is you usually have several ways to download the app. For simplicity, I will use Appbrain as an example.
As an Android app
You can get the Appbrain app in the Android market. From the application, you can search for and download any application known to the site.You are also given several ways to filter your search results.
Most of the applications you will find on Appbrain will have a QR code you can scan. If you are unfamiliar with what a QR code is, here is an example.
Leave a comment with your favorite site to get applications from.