user10601: We play with the rule one loses -> the team loses. My cheesy titled question is serious: let's try to wrap our heads around the Bughouse clock mechanics. When should one consider sitting/stalling? I imagine these ones:

I sit because the opponent mates me in the next move.
Because moving would mean giving my opponent a chance to capture a piece of mine, giving his partner a piece he needs and improves his game a lot.
To wait for a piece my opponent could handle me that could give me huge advantage.

Also, for stalling/sitting we always need more time that the diagonal opponent, if not, he could stall and we lose by time.
Are there other reasons to sit/stall?

user10894: Well, since the values of pieces in bughouse chess depends severely on the position type (e.g. a queen is often useless) you may want to stall/not play immediately when you're waiting for a specific piece to complete your strategy in general, not necessarily to win you a piece or gain some specific advantage.
E.g. you may have noticed experienced bughouse players starting with 1.Nf3 followed by Ng5 or Ne5 and sacrificing at f7. Now, when the king takes the knight, you might not reach an immediate advantage, but getting a knight could yield you a nice aggressive position.
Or another example would be waiting to get a pawn very early to disturb your opponents development as early as 2nd or 3rd move, with the goal of attacking, but also getting more space and a psychological advantage.
While we're on that, sometimes if you're playing blitz bughouse casually, chatting etc. you might want to spend some time just to get your opponent off track, since psychology plays a huge role in chess, and therefore in bughouse as well.
However, I would agree with you that on most occasions it is that you see you're getting checkmated in the next move so you let your partner play as long as he can(given that you have more time than your diagonal opponent, of course). 
That's pretty much all I can think of, I hope you find this answer useful!

user26072: I will give an (impractical but I think interesting) answer to when it theoretically makes sense to stall in Bughouse, since on a mathematical level this is a definitive factor in the game.
In particular, let a position on one of the boards be 'winning' when, assuming no further pieces are incoming from the other board, the position is theoretically won with optimal play on that board (given the board-state + pieces in hand for both players). Then there is the following lemma:
Consider players A1 vs B1 on board 1 and A2 vs B2 on board 2. If the position becomes winning for A1 on board 1 (and A2 expects A1 to successfully obtain the win), then A2 can assure the win with no further cost in game-complexity simply by stalling if the clock time remaining for A2 is greater than the clock time available for B1 plus the time A1 will need to force the win against B1.
Why? Because if A2 stalls while having less time than B1, for example, B1 always has the option of themselves stalling, and A2 needs to outlast B1 or else his flag will fall before either B1's flag falls or B1 is mated by A1.
If you (any human pair) were to play theoretically-optimal opponents, expect the game to last only briefly across both boards. Then one board falls silent with stalling; that's when you know that on the other board they've spotted a forced win.

10601: <p>We play with the rule one loses -> the team loses. My cheesy titled question is serious: let's try to wrap our heads around the Bughouse clock mechanics. When should one consider sitting/stalling? I imagine these ones:</p>

<ul>
<li><p>I sit because the opponent mates me in the next move.</p></li>
<li><p>Because moving would mean giving my opponent a chance to capture a piece of mine, giving his partner a piece he needs and improves his game a lot.</p></li>
<li><p>To wait for a piece my opponent could handle me that could give me huge advantage.</p></li>
</ul>

<p>Also, for stalling/sitting we always need more time that the diagonal opponent, if not, he could stall and we lose by time.</p>

<p>Are there other reasons to sit/stall?</p>
 10894: <p>Well, since the values of pieces in bughouse chess depends severely on the position type (e.g. a queen is often useless) you may want to stall/not play immediately when you're waiting for a specific piece to complete your strategy in general, not necessarily to win you a piece or gain some specific advantage.</p>

<p>E.g. you may have noticed experienced bughouse players starting with 1.Nf3 followed by Ng5 or Ne5 and sacrificing at f7. Now, when the king takes the knight, you might not reach an immediate advantage, but getting a knight could yield you a nice aggressive position.
Or another example would be waiting to get a pawn very early to disturb your opponents development as early as 2nd or 3rd move, with the goal of attacking, but also getting more space and a psychological advantage.
While we're on that, sometimes if you're playing blitz bughouse casually, chatting etc. you might want to spend some time just to get your opponent off track, since psychology plays a huge role in chess, and therefore in bughouse as well.</p>

<p>However, I would agree with you that on most occasions it is that you see you're getting checkmated in the next move so you let your partner play as long as he can(given that you have more time than your diagonal opponent, of course). </p>

<p>That's pretty much all I can think of, I hope you find this answer useful!</p>
 26072: <p>I will give an (impractical but I think interesting) answer to when it <strong>theoretically</strong> makes sense to stall in Bughouse, since on a mathematical level this is a definitive factor in the game.</p>
<p>In particular, let a position on one of the boards be 'winning' when, <em>assuming no further pieces are incoming from the other board</em>, the position is theoretically won with optimal play on that board (given the board-state + pieces in hand for both players). Then there is the following lemma:</p>
<p>Consider players A1 vs B1 on board 1 and A2 vs B2 on board 2. If the position becomes winning for A1 on board 1 (and A2 expects A1 to successfully obtain the win), then A2 can assure the win with no further cost in game-complexity simply by stalling <strong>if</strong> the clock time remaining for A2 is greater than the clock time available for B1 <em>plus</em> the time A1 will need to force the win against B1.</p>
<p>Why? Because if A2 stalls while having less time than B1, for example, B1 always has the option of themselves stalling, and A2 needs to outlast B1 or else his flag will fall before <em>either</em> B1's flag falls or B1 is mated by A1.</p>
<p>If you (any human pair) were to play theoretically-optimal opponents, expect the game to last only briefly across both boards. Then one board falls silent with stalling; that's when you know that on the other board they've spotted a forced win.</p>
