According to this Wikipedia page, there are 20 countries and 22 territories without a permanent natural river flowing within them.
Here is the list of those 20 countries and 22 territories that have no rivers:
- Anguilla
- Aruba
- Bahrain
- Bermuda
- Bonaire
- British Indian Ocean Territory
- Cayman Islands
- Christmas Island
- Cocos Islands
- Comoros
- Curaçao
- Djibouti
- Easter Island
- Gibraltar
- Kiribati
- Kuwait
- Libya
- Macau
- Maldives
- Malta
- Marshall Islands
- Monaco
- Nauru
- Niue
- Norfolk Island
- Oman
- Pitcairn Islands
- Qatar
- Saba
- Saint Barthélemy
- Saint Martin
- Saudi Arabia
- Sint Eustatius
- Sint Maarten
- Tokelau
- Tonga
- Turks and Caicos Islands
- Tuvalu
- United Arab Emirates
- Vatican City
- Wallis and Futuna
- Yemen