I have never seen a Bishop promotion apart from once at a tournament when one player was winning to such an extent that he promoted to have 3 bishops on the board for all to see. Underpromotion to Rook is commonplace.
Is there any use for promoting to a rook or bishop instead of a queen?

The Albin Counter Gambit is powerful and leads to short games.
It's an opening trap, the Lasker Trap. White should NOT play 4. e3? which leads to the trap. While 3... d4! gives black some positional advantages, once white can develop, the endgames are better for white given that they are up a pawn. I looked in my ECO from 2011 and all lines and informant games led to a slight plus for white.

Things are different for us mortals. OTB results against your own strength count more than theory. Lots of my books have written in the margin 'Not OTB'.
On the lighter side, I heard of a game that went down to K, B & P (not a RP) vs. K. A simple win, but the game continued. When it was time to promote, the player decided he wanted to practice the 2 Bishop mate. Only AFTER promoting did he notice that he now had 2 Bishops on the same color squares.

and a pawn checkmate to boot

Silly question, who would promote to a Bishop unless he/she already had two Bishops and wanted a third one just for fun.
Promotion to a rook usually is done when promoting to a queen would result in stalemate. A rare situation, but it does occur in some endings.

That study was posted in 2012 and still the OP hasn't bothered to correct their errors, here's the study in its original form
I don't think chess engines can solve these studies because of the difference in evaluation when promoting to a Q vs B or Q vs N. The difference in the evaluation being so great the chess engine discards the line?? If you do decide to rev up an engine jump to 8.b7 and see where 8...Kd3 takes you ;-)
@Made_in_Shoreditch
thx for the correction, I just searched for this study (since I believe that this is a good answer for the question, showing all the possibilities) and was too happy that I found it here at this site - what a luck - and posted it without checking. I did not expect to find a fake. Many thx again.

That study was posted in 2012 and still the OP hasn't bothered to correct their errors, here's the study in its original form
I don't think chess engines can solve these studies because of the difference in evaluation when promoting to a Q vs B or Q vs N. The difference in the evaluation being so great the chess engine discards the line?? If you do decide to rev up an engine jump to 8.b7 and see where 8...Kd3 takes you ;-)
you can get by just fine without underpromoting

I promote to rook of I want to ladder matter just so I don't get an accidental stalemate
Just check if it makes stalemate before promoting? I don't see the point here
I promote to rook of I want to ladder matter just so I don't get an accidental stalemate
Just check if it makes stalemate before promoting? I don't see the point here
In a time pressure situation it may make more sense to quickly promote to a rook instead of spending time seeing if a queen is stalemate.
I mean, if the option's there, then there has to be a use for it, right?
It is conceivable that a Queen promotion could create a stalemate. The opposition king would need to be two squares away from the new queen, one rank away from the queen, and not on its diagonal, and have no other legal moves on the board Then an underpromotion would be appropriate.