I can think of a few actually. Like a joke, or just a recording of something funny or unusual ...or send someone a ring tone or sms tone...ya know..that kinda stuff.
Tho it would be better to just email it.
I know there is a tweak from Cydia called SendAny and RecieveAny, that allow you to attach literally "any" type of file to an iMessage message...and can send any type of file via iMessage to another iDevice that also has the tweak.
If coarse you must be jailbroken.
SendAny cost money....don't remember how much. I think $2.