Citizens of US, EU and CIS countries, Canada, Chile, Norway, Switzerland, Japan, Turkey, Malaysia 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.
Citizens of EU, Liechtenstein, Monaco and Switzerland can use a national ID card instead of a passport, but only if it is in card format. The old rule that ID cards must be biometric seems to still apply at the Ungheni border crossing used by night trains from Bucharest, where EU nationals holding non-biometric ID cards have recently been arrested and deported.
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. Recently June 2015 travelers, whom cross in to Moldova via Transnistrian are required to obtain a entry stamp within 3 days of arrival, otherwise a "small" fine amount unknown can be given to the traveler. The entry stamp can be collected at the airport and possible another location in Chisinau.
There are regular buses connecting Chişinău with Bucharest, Kiev and most major Romanian and Ukrainian cities. There are 5 to 6 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.
Kiev, 2 daily, 250 lei, 12 hours
Moscow, 4 daily, 700 lei, 30 hours
Odessa, 20 daily, 120-150 lei, 5 hours
Sevastopol, daily 430 lei, 18 hours
Brasov, 5 daily 200 lei, 12 hours
Busiest air connections exist to Bucharest, Istanbul, Moscow, Munich, Timisoara, and Vienna. Prices are relatively high. The cheapest tickets can be bought to Bucharest, Istanbul, Kiev and Moscow. Low-cost airline Wizz Air operates flights to Rome, Milan and Venice, and will commence flights to Bologna and London Luton in Autumn 2015. 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.
Although the country is landlocked, there is a ferry service between Giurgiulesti in Moldova and Istanbul, Turkey, plying the river Danube to reach the Black Sea. They leave Giurgiulesti every Monday and arrive at Istanbul the following Wednesday. It's not certain if this ferry service is only limited to the high season or not.
Much cheaper than flying, but about twice the cost of the bus but arguably more comfortable the overnight train may be considered a valid option. There are daily trains from Romania and Ukraine. The train from Bucharest is about USD40. 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.