usually bishop and knight are better than one rook for me but the game's current position decides. if u r close to mate then it can be taken, if u r in the middle of the game i recommend not to take (usually ! not always! listen ur insticts! )
Would you have a rook, or a bishop and a knight?

normally during endgame i always do this if i have the chance (since it is much easier to mate with a rook than a bishop + knight) however during midgame a bishop and knight can work together with quite good effect so its really up to personal taste
I repeat what I said on another topic:
There is a nice series of articles about this topic, written by a GM here on chess.com:
part 1: http://www.chess.com/article/view/a-rook-or-two-minor-pieces
part 2: http://www.chess.com/article/view/a-rook-or-two-minor-pieces-part-two
part 3: http://www.chess.com/article/view/a-rook-or-two-minor-pieces-part-three
test: http://www.chess.com/article/view/a-rook-or-two-minor-pieces-test-your-skills

In 90% of the cases it is better to have the bishop and knight but what really decides is the particular position.
The question as posed is almost without meaning. [because you have to know the position to answer the question]

I prefer to play with the bishop and knight because like playing with more pieces rather than powerful ones.

Well obviously 3+3 > 5
But if you have to ask, then apparently this primitive measure isn't enough. As others said usually the two minors are better, but it always depends on the specific position. The trick for evaluating trades is to note how useful the remaining pieces are. If your remaining pieces are more active (and will remain more active) then it doesn't matter if you gave up a queen for a pawn, your position is better.

That position is extremely illegal, but I would have to guess that the best move is d5, which doesn't involve a capture, or a knight and bishop for rook.

I go for a knight and a bishop for a rook because almost always, bishop and knight can have much better activity for a rook itself.

And one must not underestimate the power of the two minor pieces. B+N is almost always better than a rook, usually even better than a rook + pawn and even sometimes stronger than a rook and two pawns. I had one position where 2B easily held a draw vs a rook in 3 pawns, which while slightly different still illustrates the power of the 2 pieces.

In a game, I normally have the chance to take my opponents rook in exchange for a bishop and a knight. What would you do + why?
In a game, I normally have the chance to take my opponents rook in exchange for a bishop and a knight. What would you do + why?
Thanks
Pastakinglegend