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 (http://www.mfa.gov.md/ent...). 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" in the east of Moldova bordering 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 Ukraine, Transnistria and the rest of Moldova usually handle negotiations at the border well, collecting passports and negotiating with Transnistrian authorities. Also, there is no Moldovan border check between Transnistria and the rest of 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.
By plane
Busiest air connections exist to Bucharest, Budapest, Istanbul, Moscow, Munich, Timisoara, and Vienna. Prices are relatively high. The cheapest tickets can be bought to Bucharest, Istanbul, Kiev and Moscow. Moldova has three air companies. It is also possible to get relatively cheap tickets from Munich with Lufthansa/Air Moldova. They were around 190 Euro return in May 2010.
By train
Possibly the cheapest way to get into the country is to take the overnight train. There are now daily trains from Romania and Ukraine. Train from Bucharest is about US$40. Since flights into Bucharest cost approx. US$200 less than those into Moldova, this is the best option if you have the time. This service was suspended following 2009 political turmoil and it's unknown whether it was resumed, be sure to check. At the border crossing the cars are lifted individually onto larger gauge wheels to fit Moldovan tracks. Crossing the border from Ukraine is smoother, the track width is similar to Moldovan tracks.
By bus
There are regular buses connecting ChiÅinÄu with Bucharest, Kiev and most major Romanian and Ukrainian cities. There are 5 to six buses per day to and from Bucharest. Due to a longer stay at the border the trip takes around 10 hours. Be aware that there is a basic toilet at the border, however most coaches do not make any other stops.You will also be able to travel to most European cities by bus with Moldovan bus companies.When coming by bus one should be sure to use a frontier with a non-stop visa issuing office.
Kiev, 2 daily, 250 lei, 12 hours
Moscow, 4 daily, 700 lei, 30 hours
Odessa, 20 daily, 90 lei, 5 hours
Sevastopol, daily 430 lei, 18 hours
Brasov, 5 daily 200 lei, 12 hours
By car
When coming by car one should be sure to use a border crossing with a non-stop visa issuing office. You will have to pay a small road tax at the border.