Do we know of any living forms on Earth that could continue to live on Mars?
Yes, research studies that were conducted have found that methanogens (microorganisms) is able to survive in conditions similar to Mars (reference). Another study conducted has also concluded that some lichen and cyanobacteria is also capable of survival. Surprisingly, they were also found to be active (reference).
There is speculation now on whether organisms from earth have been accidentally transported to Mars on the Mars Curiosity Rover which would be funny or a cause of concern, depending on how you look at it (reference).