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