According to this CNET article, a TIFF image cannot be larger than 4GB. However, a group of medical imaging specialists have created their own TIFF format which has no practical size limit. Called BigTIFF, it is in the public domain, but it has not yet been officially released.
There are some examples on the BigTIFF website, but look at this one. This image is 12.78GB in size. Click on the percentage at the bottom of the image. Continue to resize it to 100%. It is incredible!