What do you do as black when white plays d4?  For some reason I always have problems against d4.

Against the mainline (2.c4) stuff I play the benko gambit.

What sort of opening(s) do you play and why do you run into trouble?

 

What style to you like against e4? 

Honestly, I've played a bunch of openings to try and find one I'd have success with.  I like to castle early, so sometimes I'll fianchetto the bishop and get the knight out quickly.  Then I'll try and develop the other side of the board and white already seems to be attacking me or blockading my bishops.

I 1.d4 d5 is the simplest response for black, personally I like the Slav, Queens Gambit Accepted, and the Albin counter gambit.

I play d6 in order to throw people off, especially book players.  Then I follow up with a Slav, or g6 modern (with the possibility of a KID).

I play the Semi Slav.  It is very solid, but has dynamic chances available.  It appeals to many of today's best Grandmasters such as Vishy Anand.

Its my experience when I play 1 d4 I face a wider variety of openings than when I play 1 e4, due to the popularity of the sicilian against 1e4.

If you're getting smothered in 1.d4 games (not uncommon) go for openings that put you in the center of the board with white.  Play the Slav, Tarrasch, Nimzo/Bogo, and avoid Kings & Queen Indian, etc. Fight for the center.