Has there ever been a recorded game of Scrabble where somebody made a play for 0 points? The only way to do this would be to play a single blank onto the other blank. I can think of 2 reasons why someone might do this: It’s the very last tile and all the squares are too awkward to play any single letter on except the one by a blank; or near the end of the game a blank appears adjacent to a TWS and you know the opponent has tiles he can leverage into a huge score, the only tile you have which can prevent it being another blank. People inexperienced/unskilled enough to make really bad plays, or somebody just messing around as he has already won/lost the game are not good reasons.
The closest I got was just the other day. Played my last tile - a blank - on a one-pointer. In tournament play, I find it highly unlikely, but not impossible.
Joe
I have a hard time picturing a Scrabble board so cluttered that the only place to put a blank would be by another blank.
I would think a play like you described would be so spectacularly odd that it would have been talked about a lot (well, in Scrabble player circles anyway), so if you haven’t heard of it or couldn’t find it with a Google search the answer is probably “no”.
As for theoretical situations like you describe: the first instance seems incredibly unlikely, maybe even impossible to construct. A board that has no room for single tile play where a blank tile would score ANY points, other than next to the one and only other blank tile (locked in with whatever letter value was assigned to it when played)?
The second one makes it more plausible - that there ARE other places to play the blank tile, but are strategically less attractive. There however it would only make sense in the end game, because otherwise you’d probabbly be better off saving the blank tile to assist in dropping your own terrifying bingo or high scoring combo in a future move. In any case I can’t think of any effective “blocking” words I’ve put down that were of a single tile variety.
I think the only circumstance that is “likely” to come up would be like wheresgeorge04 described: using a blank as your last tile to finish a game where you don’t need the points (win or lose), so just for style, you choose the two-letter word that is next to the other blank tile to score zero points.
Well, now I have to try to do it! 
Watch out, Joe!
I’m going to assume that “pass” and “tile swap” are not acceptable answers.
A similar question is what the fewest points anyone has ever gotten is for a bingo. I think the theoretical minimum is 56. You have to play 7 tiles, so at least 5 points in your tiles plus the 50 point bonus. But you also have to either be making the first play of the game (so you’re on a DWS) or connecting to at least 1 tile already on the board, so 8 tiles have to score, for a minimum of 6 plus the 50.
You go ahead and make as many zero-point plays as you desire.
Joe
56 sounds right. Hook letter is a blank, played on a blank, with six one-point tiles. I’m pretty sure I’ve done 58 before…
Joe
Not if I’m kicking your ass already… 
We both have.
Is there any place on the board you could fit that bingo, without hitting a bonus tile, though?
The board on Wordsmith has 7 blank spaces in a row horizotally, next to a DW on each end. The board on Wordfeud doesn’t.
I’m pretty sure Wordsmith is the traditional Scrabble board, but I’m not positive.
Get the blank tiles on the double letter spaces and you’re covered.
So, no, it’s impossible to do unless you use the blank on the bonus square.
Can’t find an image of the Wordsmith board, but it’s different, and DOES have (it looks like) two places with seven consecutive non-bonus spaces.
Joe
There’s an even more implausible way to score 0 points, btw, which is to play a two letter word as the first play of the game using two blanks. That, however, would clearly never happen barring eccentricity.
If one of the double word score tiles closest to the center tile was already used, you could play across that and not hit any other bonus squares.