It often leads people to write code like this:

    try {
        // do stuff
    } catch (TheCheckedException ex) {
        // ignore it
    }

then the code continues even though it could be in a bad state if an exception did occur.

It's a much better solution to let it propagate up the call stack until it can be dealt with appropriately (e.g. by ending the application, giving a 503 error on a web page request, etc.) Unchecked exceptions will propagate up the call stack by default if you don't do anything, making it harder for people to write bad exception handling code.