Logo descriptions by Sagan Blob Logo captures by Eric S., Gilblitz112 and CokeFan12 Video captures courtesy of Eric S.
Logo: On a red background, a crude drawing of a tiger with the jaw wide-open zooms in. Then, "A TIGON PICTURES RELEASE" wipes one by one, with "A" and "RELEASE" above and below "TIGON PICTURES".
FX/SFX: The zoom-in and the wiping.
Variant: A version with blue background and different font exists.
Music/Sounds: A patriotic horn sounder. Sometimes, it's silent.
Availability: Found on The Body Stealers and the Blu-Ray release of The Magnificent Seven Deadly Sins. The blue background variant can be seen in their later movies, such as Au Pair Girls.
Scare Factor: None to minimal.