TIFF is a pretty odd and useless format. It also doesnt put anything new on the table.
Interesting formats (for games) are things like:
-raw 8:8:8:8, 8:8:8, 8:8, 5:6:5, 5:5:5, 5:5:5:1, 4:4:4:4 (TGA to some extend and DDS)
-lossy rgb/grayscale (JPG)
-indexed rgb (TGA/DDS)
-indexed rgba (DDS)
-precompressed dxt1-dxt5 [also lossy] (DDS)
(And there is also some normal map stuff, but I havent take a look yet.)
As long as you dont have a good reason to use TIFF, I wouldnt bother.