At times when I visit some websites they declare that I have won a prize for being the 100,000 or 1,000,000 guest on that site, and they offer a holiday cruise in Florida with cash prize of about 2,000 dollars, is it permissible to accept this travel offer, or the cash offer, or both.

All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger. We ask Allaah to exalt his mention as well as that of his family and all his companions.

There is no harm in accepting the money-prize since you did not pay anything to obtain this prize or to enter a competition, as this is just for being guest number such and such. As regards accepting the free travel to that country, then we do not consider that it is permissible to accept it. Travelling to this country has many disadvantages and harms on one's religion. Such a trip is usually organized to visit bars and places of dissoluteness, like hotels and tourist places where there is much disobedience. Therefore, it is not permissible to accept this kind of prize without the intention to call people to Islam and while being safe from temptation and have the ability to practice your religion.    

Allaah knows best.