I have a Kuwait visa, obtained from a hotel in Kuwait, with my old passport number. But as the validity of the present passport is expiring within 6 months, I got a new passport with a new passport number. Can I travel with the same visa or do I have to obtain a new visa with my new passport number?
Bring the old passport with you along with your new passport (hopefully you still have it) and you will be able to enter. This applies to all other countries provided that the page where the visa is not cancelled (usually by writing a big X or by puncturing it in the sides).
Update: Always remember to ask the authority to handle you the old passport when you renew it and do not forget to mark the valid visas page before renewal as @Jonas commented.