I dont get exceptions

Most every programming language has exceptions, but I dont understand the need for them over regular error checking code. I took a Java course and we just used regular if statements to check input values from IO and it worked perfectly fine. Ive heard exceptions are not allowed in highly critical code as it makes unpredictable runtime logic. Can someone tell me what exceptions offer beyond error checking code that you could write on your own?

>>6
call/cc is indeed the most general (and theorethically elegant) solution to exception handling, but maybe it's a bit too general and costly for general-purpose exception handling. It also does not play too well with UNWIND-PROTECT-like constructs, without crippling one construct or the other.