Veritable Tower of Babel like CDP or Transport

Have you ever had CD players or transports that have trouble reading a specific or some CDs, while the same CD will be read by a different model, without any problems? I am running out of rack space and so far, I got a brand new code free DVD player used along a Bel Canto DAC-1 and when I received a new CD yesterday, it began to freeze, in certain instances....I loaded the same CD in a 3 CD charger of a minisystem and it read it flawlessly. Is there a CD player that will be able to read almost anything, I do not mean SACD or DVDA, but anything that was recorded either in a CD press plant or burned in someone's machine, without freezing up or mistracking. I am looking for a veritable Towel of Babel CDP or transport, that will satisfy my audio urges until the next format comes around.