Your toes should be slightly curled in climbing shoes. This gives you extra power and accuracy when standing on your toes on small edges. It also allows you to be more precise with your footwork by being able to stably place your foot on holds and in positions that would normally be much more difficult.
Having curled toes also helps you feel the holds better so that you are better able to trust your feet on poor foot holds.
The amount at which your toes should be curled though depends on the climbing shoe, and on your comfort/pain level. Just like the climbing shoes themselves, your toes should not be in pain and should not be painfully curled down. For many shoes, the curl will be a very slight curl where the tips of your toes are slightly pointed downwards instead of straight forward. In other shoes, the curl may be more aggressive, with the tips of your toes pointing directly down.
