I'm using KMplayer with this option, but I am looking for alternatives, and it's the only one I know with this feature.
I am not talking about just removing a file from the playlist, but the physical deletion of video being played.
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Winamp can (sort of) inherently. Having it as a shortcut is on their wishlist (since at least 2008).
Press the little minus button in the lower-left corner of the playlist (assuming default Bento skin):
If you prefer the Recycle Bin:
Now add the Playlist File Remover plugin, as it supports deleting from disk if you press Next before the song is finished. You can also set a Global Hotkey in Winamp for Next so you could define the hotkey to your liking.