Bishop G6

In many of my games I come in the following (or a similar) position:

There are multiple possibilities:
- Take the white bishop on E6
- Move the bishop back to B3
- Something else?

I usually move the bishop back because I don't wish to open up the f file for the rook. However, I'm not really sure what the right thing is to do. What would you suggest?

I'd not recommend taking on e6. You can play Bb3, or 0-0, both of which are better than taking, my opinion. 

This is from a perspective of having easy play, by the way. The reason Bxe6 I wouldn't recommend is because now black knows exactly what to do: ...Qe8, ...Qh5, doubling rooks on the f file, and attacking. 

Obviously all 3 options are objectively equal, and it shouldn't matter which one you play. At your level, someone will probably blunder something, and the game will end because of that. 

I got all my squares wrong... sorry about that.

I always move the bishop back, otherwise my pawn structure would be damaged if my bishop was taken or I would lose the d5 and f5 squares if I exchanged bishops and allowed a pawn on e6. I usually want a piece either on d5 or f5.

Thanks for the input! I'll be sure to try it out in future games.

Always castle before moving the king -- at least in most games.

I guess that in that particular situation (diagram #1) I would chop the bishop on e6. This is because of two reasons:

1. I have NOT castled short yet, so I don't bother that much about the open f-file and the queen switching to g6/h5.

2. After exchanging bishops at e6, I can also remove Black's other bishop from the board with Nc3-a4, a very typical idea in such positions (with both colors).

But of course, the right decision is ALWAYS dependent on the actual position. Under other terms (e.g. white having castled kingside and/or Black's pawn being on a6) things may well change.