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I suggest keeping at least three month's worth of credit card statements before discarding them. You never know when you're going to need to reference the information.
I personally keep my credit card statements for a period of 12 months before shredding and discarding them.
It is okay to file all of your credit card statements together, as long as you keep them organized. I use an accordian file folder with 12 different slots. Each month I put the statements for that particular month in the appropriate slot. It makes it much easier to keep track of everything.