Visas are not required by nationals from Armenia, Austria, Azerbaijan, Belarus, Belgium, Bulgaria, Canada, Croatia, Cyprus, Czech, Denmark, Estonia, Finland, France, Georgia, Germany, Great Britain, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Kazakhstan, Kyrgyzstan, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Russia, San Marino, Slovakia, Slovenia, Spain, Sweden, Switzerland, Tajikistan, Ukraine, UK, USA and Uzbekistan
Everyone else may need to obtain an invitation and head to an embassy.
Visa Information for Moldova
Foreign embassies in Moldova
Visas for the Republic of Transdnister (Trans-Dniester) are not required when entering from Moldova, all you need is a current passport.