Are you talking about unhandled exceptions?
Do
process.on('uncaughtException', function (e) {
console.log(new Date().toString(), e.stack || e);
process.exit(1);
});
Of course you'll have a nicer time parsing the date with something like momentjs
For exceptions you handle yourself, use a logging library such as winston, which allows you among many other things, to pick a format.
Update
See what the node docs have to say
Do not use it as the node.js equivalent of On Error Resume Next. An unhandled exception means your application - and by extension node.js itself - is in an undefined state. Blindly resuming means anything could happen.