I have never felt secure depositing into a ATM although I guess cheques are safe.
Me neither, although these days the ATMs scan the checks, right? In the old days you had to put it in an envelope and hope for the best.
The thing I hate most is when well-meaning relatives send birthday checks (to my kids, primarily) for $20. So you have to make a whole trip to the bank (or, if you dare, at least an ATM), when a) a $20 bill is pretty safe to mail and b) even if it did get lost or stolen you're only out $20. My stepmother boldly sends my kids $100 bills for big occasions and I'm really grateful.