While I've had this problem with my cards stored in binders I can't say that the cards themselves were damaged. I did have problems with some of the Inkworks binders where the front and back plastic split along the seam. This seems to happen with the puffy binders such as 'The Simpsons'.

Thanks for the tip Salama, you have some very nice cards there

The only time I have had problems with the Inkworks binders splitting is when they have been sent to me already that way, so now I am very careful to ask questions about split sides especially if there is nothing said in the listing about condition.
All I ended up doing at the moment is properly filling up two of my Ultimate Collection Binders full instead of have all four of them only 2/3's full.

I also use the ultropro padded binders.

Keeps the all nice and straight.
Haven't found a good enough one for all my walking dead costume cards though, currently they sit in individual sleeves in a box.