I can't install or update Apps from Play Store: Error 905. How to fix?

Suddenly (after a Play Store update?) I can't install or update any Apps. I always get error code 905 when I try to do so. How can I fix this?

Answer

Uninstalling all Play Store (Market) App updates fixed it for me.

Go to Settings -> Applications -> Manage Applications -> All tab -> Google Play Store and uninstall the updates. This will leave you with an older version of the app, which is probably named "Market". Then you should be able to install or update apps. After a while, the Play Store update will be installed once again, but you still will be able to install or update Apps.