Support for tiff files was removed from pdftex and pdflatex some time ago. However, TeXShop has a menu command "Convert tiff" which converts tiff files to png format, which pdftex and pdflatex understand.
Although pdftex and pdflatex understand graphic files in pdf, jpg, and png formats, they do not understand the eps format. Many old TeX projects used eps illustrations because dvips understood it. Since 2011, TeX Live will automatically convert eps files to pdf format during typesetting, provided the source document includes the graphicx package. This conversion does not require use of the "--shell-escape" flag, which presents security issues.