Citizens of US, EU, CIS countries, Canada, Norway, Switzerland, Japan do not need a visa to enter Moldova and can stay in the country for up to 90 days within a six month period without registration . Citizens of other countries must either obtain visa in the nearest Moldovan embassy or alternatively could obtain visa on arrival in Chisinau airport and on some land border crossings provided that officially endorsed invitation letter from Moldova is obtained beforehand.
If, being a motivated person, you are coming into Moldova via Ukraine, be aware you may be crossing Transnistria. Some buses from Odessa go through Tiraspol, while others go around, exchanging the two border crossings with more time on the road. Transnistria is an unrecognised "state" between Moldova and Ukraine, which broke off from the country after a war in 1992. As of this year (2010) there are few issues for Westerners in crossing Transnistrian borders by bus, although foreign travellers have experienced problems in the past. There is, however, a small chance that foreign tourists may be asked to pay bribes, although the buses which travel between Moldova, Transnistria and Ukraine usually handle negotiations at the border well, collecting passports and negotiating with Transnistrian authorities. Also, there is no Moldovan border check between Transnistria and Moldova as Moldova does not recognise Transnistria as a state, so you might have some explaining to do when you try to leave Moldova without an entrance stamp.