Only a small change to your phone is needed to install a non-Market Android app.
Before you start browsing and downloading non-Market apps via your Android phone, go to Settings > Applications and under Application Settings tick the box Unknown sources. This will allow the install of non-Market applications, so once the phone has accepted this change, you can flip back to your browser and carry on looking for a new app to download!
The reason for this rather strange feature is that, as described above, apps in the Android Market are listed as they are submitted, without any testing. Only the feedback from other users can give any idea as to whether the app is safe or indeed fit for purpose. In contrast, non-Market apps from the reputable websites listed above have been tested.