Android - How to remove apps from "all downloaded" in Play Store

No, it's not possible. The android market is plagued with issues like this one.

As of version 3.9.16 you can finally now remove applications from the "all" tab in the my apps list. You can even select several apps at once by long pressing one, then selecting the others.
These apps are removed from the Website too.

^{Source: Android Police}

This was left as an edit to another post by an anonymous user, but should be its own answer.

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Go to the Google Play app on your mobile phone and go to Menu -> My Apps, then swipe across to All Apps. Delete the app from there using the symbol button on the right, and the app will also delete from the online Play Store list.

In order to delete several applications at a time, long-press an application until a blue top bar appears; then short-press some other applications, and you will be able to delete all selected applications by pressing the deletion symbol in the upper-right corner, in the blue bar. This is especially practical because you jump to the top of the list after deleting an application, and the list is only sorted by date of first installation—at least at this moment.

It is possible to remove multiple entries from the All list of apps with the new version of Google Play.

Long press on the first app to remove and a header bar will appear with a check mark and a delete symbol. Tap all the apps you want to remove and then tap the delete symbol.