In order to know what kind of visa you will need to enter the Republic of Panama, please check below to see which of the following options applies to your passport.

Countries with NO VISA required
America : Chile, Argentina, Bolivia, Uruguay, Costa Rica, El Salvador, Honduras, Paraguay, Brazil, Nicaragua, Guatemala, Colombia.
Europe : Germany, Bulgaria, Hungary, Australia, Italy, Poland, Spain, Portugal, United Kingdom, Países Bajos, Greece, Finland, Luxemburg, Belgium, France, Switzerland, Lithuania, Letonia, Chipre, Andorra, Denmark, Eslovaquia, Estonia, Ireland, Iceland, Liechtenstein, Monaco, Norway, Czech Republic, Romania, Malta, San Marino, Vatican.
Asia : Singapore, Israel, Republic of Korea (South Korea).

Countries that require STAMPED VISA
America : Ecuador, Peru, Dominican Republic.
Europe : Belarus, Croatia, Georgia, Moldavia , Russia, Ukraine.
Asia : Vietnam, Maldives, Mongolia.
Oceania : Fiji, Marshall Islands, Salomon Islands, Kiribati, Micronesia, Narú, Palau, Papua New Guinea, Samoa Occidental, Tonga, Tuvalu, Vanuatu.
Africa : Angola, Botswana, Cape Verde, Cameroon, Gabon, Ghana, Islas Comores, Madagascar, Malawi, Mauricio, República Centroafricana, República del Congo, Santo Tomé y Principe, Seychelles, Suaziland, Togo, Zimbabwe.

Countries that require either STAMPED VISA or TOURIST CARD
America : Canadá, Estados Unidos, México, Belize, Antigua y Barbuda, Bahamas, Barbados, Dominica, Granada, Jamaica, San Cristóbal y Nevis, Santa Lucía, Trinidad y Tobago, Guyana, Venezuela.

Countries that require AUTHORIZED VISA
América : Cuba, Haiti, Suriname.
Europe : Albania, Bosnia-Herzegovina, Macedonia, Serbia & Montenegro.
Asia : Afghanistan, Saudi Arabia, Armenia, Azerbaijan, Kingdom of Bahrain, Bangladesh, Bhutan, Brunei, Camboya, People's Republic of China, United Arab Emirates, India, Indonesia, Iran, Iraq, Jordan, Kazajistan, Kirguistan, Kuwait, Laos, Lebanon, Malaysia, Myanmar, Nepal, Oman, Pakistan, Qatar, People's Democratic Republic of Korea (north Korea), Syria, Sri Lanka, Tajikistan, Turkmenistan, Uzbekistan, Yemen, The Philippines, Turkey.

** IMPORTANT NOTICE ---Special Case for the AUTHORIZED VISA
As of July 21, 2009 Executive Decree No. 248 has come into effect. This new law states that

"Holders of a passport that is valid for at least 6 months and has a valid visa to one or more of the following countries: United States of America, Canada, Australia, United Kingdom or ANY of the member countries of the European Union, which has been used at least once to enter that country, can enter the National territory by obtaining a Stamped Visa or equivalent REGARDLESS of their Nationality."

For further information please access the following link which contains a copy of the law decree:
http://www.gacetaoficial.gob.pa/pdfTemp/26328/19022.pdf