I recently had a deck of custom cards printed at MakePlayingCards. They accept bmp,png,tiff and jpg images at a minimum resolution of 300 DPI. I have a bunch of SVG vector images that I can convert to whatever DPI I need, but I thought 4 times the minimum would be more than enough, and used 1200 DPI png images.
They came out looking fairly well, but grainy in the detailed portions. I know the resolution needs to be higher, but I don't know by how much. I would like to print at the best possible DPI without making the images overly large for no good reason. The MakePlayingCards site does not mention what the maximum resolution their printers can print is, nor can I find that sort of information on other card printing sites.
I don't even know a good ballpark for this number, so the maximum DPI of any reputable playing cards is an acceptable answer. eg. The DPI at which Bicycle cards are printed is x.