Cyprus is broken in half, the North of the island has the same visa regulations as Turkey (listed under middle east on this site), while the south has its own visa regulations.
No visa is required for tourists for a stay of up to 90 days from:
Andorra, Antigua and Barbuda, Argentina, Australia, Austria, Bahamas, Belgium, Barbados, Bermuda, Brazil, Brunei Darussalam, Bulgaria, Canada, Chile, Costa Rica, Croatia, Czech Republic, Denmark, El Salvador, Estonia, Finland, France, Germany, Greece, Guatemala, Holy See, Honduras, Hong Kong, Hungary, Iceland, Ireland, Israel, Italy, Japan, Latvia, Liechtenstein, Lithuania, Luxembourg, Macau, Malaysia, Malta, Mauritius, Mexico, Monaco, Netherlands, New Zealand, Nicaragua, Norway, Panama, Paraguay, Poland, Portugal, Romania, Saint Kitts and Nevis, San Marino, Singapore, Slovakia, Slovenia, South Korea, Spain, Sweden, Switzerland, Taiwan, United Kingdom, United States of America, Uruguay, Venezuela.
If you have a stamp from Northern Cyprus in your passport, you may not be able to enter Southern Cyprus. The rule is no longer enforced but the border guards in the North who will stamp your entry and exit stamps on a separate piece of paper if you ask.
Cyprus information
Cyprus embassies