I wish to know which countries do not have extraditon treaties with
the United States.

You may want to take a look at this previously answered question.

http://answers.google.com/answers/threadview?id=27692

Afghanistan, Algeria, Angola, Bahrain, Bangladesh, Benin, Bhutan,
Botswana, Brunei, Burkina Faso, Burundi, Cambodia, Cameroon, Cape
Verde, Central African Republic, Chad, China, Comoros, Djibouti,
Equatorial Guinea, Ethiopia, Gabon, Guinea, Guinea Bissau, Indonesia,
Iran, Ivory Coast, Jordan, Kuwait, Laos, Lebanon, Libya, Madagascar,
Mali, Maldives, Mauritania, Mongolia, Morocco, Mozambique, Nepal,
Niger, Oman, Philippines, Qatar, Rwanda, Samoa, Sao Tome e Principe,
Saudi Arabia, Senegal, Somalia, Sudan, Syria, Togo, Tunisia, Uganda,
USSR, United Arab Emirates, Vanuatu, Vietnam, Yemen, Yemen South,
Zaire & Zimbabwe

"Countries which do not have extradition treaties but do maintain
diplomatic relations with the US are Afghanistan, Algeria, Armenia,
Bahrain, Bangladesh, Bophuthatswana, Brunei, Burkina Faso, Burundi,
Cameroon, Cape Verde, Central African Republic, Chad, China (People's
Republic of China), Ciskei, The Comors, Cote d' Ivoire, Djibouti,
Equatorial Guinea, Ethiopia, Gabon, Guinea, Guinea-Bissau, Indonesia,
Jordan, Korea (South), Kuwait, Laos, Lebanon, Madagascar, Mali,
Marshall Islands, Mauritania, Micronesia, Maldova, Mongolia,
Mozambique, Myanmar, Namibia, Nepal, Niger, Oman, Philippines,
Principe and San Tome, Qatar, Russian Federation, Rwanda, Saudi
Arabia, Senegal, Sudan, Syria, Togo, Tunisia, Uganda, Western Samoa,
Yemen, Zaire, and Zimbabwe.

Countries which have neither diplomatic relations nor extradition
treaties with the US are Andorra, Angola, Bantu Homelands, Bhutan,
Bosnia, Cambodia, Ciskei, Cuba, Iran, Korea (North), Libya, Maldives,
Serbia, Somalia, Taiwan, Transkei, Vanuatu, and Vietnam."