In Mexico, the most common ones are:
"Ya, ya."
Depending on the tone, it goes from saying: "don't worry, everything will be alright", to: "you're making too much drama, stop it".
To children, after a little accident, a scare or things like that, we often say "ya pasó". It's like saying: "The bad thing is over. Everything's alright now".
Both expressions usually go with a hug or a soft pat on the back.