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Updates: 

On 2014-11-03, ISO issued an update to ISO 3166-2, changing the name of Tighina to "Bender [Tighina]."

Transnistria is de facto independent, but is included in Moldova by ISO standard 3166. It uses Russian as the main language on its official websites, and the Cyrillic alphabet for its version of the Moldovan language. Internally, its name is Pridnestrovskaia Moldavskaia Respublika (Pridnestrovie). The name has political implications: Transnistria means "land across the Dniester", viz. from Moldova; Pridnestrovie simply means "land by the Dniester". Its capital is Tiraspol, and it is divided into seven administrative-territorial units, as listed here. Bender and Dubossary correspond to divisions of Moldova, and may be partitioned between the two territories.

The result of the reorganization of Moldovan territory in 2003 is reflected in Newsletter II-2, an update to the ISO 3166-2 standard, dated 2010-06-30, and in FIPS Publication Change Notice No. 10, affecting FIPS PUB 10-4, dated 2006-03-23.

Change Notice 8 to FIPS PUB 10-4 is dated 2002-06-28. It changes the name of Dubăsari to Stîngă Nistrului, which is also the name used for it in the ISO update. I've concluded that the name Dubăsari is obsolete.

ISO 3166-2 Newsletter Number I-2 was published on 2002-05-21. It completely revises the list of subdivisions of Moldova. It shows Moldova divided into one unitate teritorială autonoma (autonomous territory), one municipiu (city), one unitatea teritorială (territorial unit), and nine judeţul (counties). The header for the Moldova entry incorrectly states that there are ten counties; the 10 is corrected to 9 in ISO 3166-2 Newsletter Number I-3, published on 2002-08-20. Taraclia county is not shown in Newsletter Number I-2, but is added in Newsletter Number I-4, published on 2002-12-10.

Change Notice 4 to FIPS PUB 10-4 is dated 2000-02-25. It shows Moldova divided into ten judeţul (counties) and one unitate teritorială autonoma (autonomous territorial unit). If they are the same divisions as those predicted by Tass in source [6], the Dniester region would have to be the same as Dubăsari county.

I have seen a series of Moldovan statistical yearbooks. Source [1] clearly shows that the divisions of Moldova on the primary level were ten counties, one city, one autonomous territorial unit, and one other unit which is verbosely described as Unităţile administrativ-teritoriale din partea stîngă a Nistrului, cărora li se pot atribui forme şi condiţii speciale de autonomie (Administrative-territorial units from the left side of the Nistru (Dniester) River, which could be entitled to special formations and conditions of autonomy). I accordingly decided to split Chisinau city from Chisinau county (former HASC code MD.CE) in the table for 1999 under Change history.

Country overview: 

Russia acquired the eastern part of the principality of Moldavia from the Ottoman Empire in the 19th century. It became the guberniya of Bessarabia, consisting of all the territory between the Prum and Dniestr Rivers east of about 26°45' East. Bessarabia proclaimed its independence on 1918-01-24, in the chaos of World War I. It united with Romania two months later. The merger was ratified by the Paris Peace Conference in 1920. The Soviet Union asserted a claim to the territory. Unable to prevail, it established a Moldavian Autonomous Soviet Socialist Republic (capital Balta from 1924 to 1929, then Tiraspol) on the eastern side of the Dniestr. After the Molotov-Ribbentrop Pact, the Soviet Union and Germany carved up the intervening territory. In 1940, the Soviet Union moved in and annexed Bessarabia and Northern Bukovina from Romania. On 1940-08-02, the Moldavian Soviet Socialist Republic was created. It contained about 28,000 sq. km. of Bessarabian territory and 3,400 sq. km. of the Moldavian A.S.S.R. The remaining pieces - Northern Bukovina, 4,900 sq. km. of the Moldavian A.S.S.R., and 17,600 sq. km. of Bessarabia, including the districts of Belgorod Dniestrovskiy, Hertza, Hotin, and Izmail - became part of the Ukraine. Although Romania re-occupied this area during the war, the Soviet Union took it back in 1944. Moldavia once again declared independence on 1991-08-27, taking the name Moldova. More recently, the part of Moldova east of the Dniestr has formed a breakaway government, Transnistria, which has not been recognized by any other country.

Other names of country: 

1. Danish: Republikken Moldova (formal)
2. Dutch: Moldavië, Republiek Moldavië (formal)
3. English: Republic of Moldova (formal), Moldavia (obsolete)
4. Finnish: Moldova
5. French: Moldavie f, République f de Moldova (formal)
6. German: Moldawien n, Moldau f (obsolete)
7. Icelandic: Moldavía
8. Italian: Moldavia f, Repubblica Moldova (formal)
9. Norwegian: Moldova, Republikken Moldova (formal)
10. Portuguese: Moldávia, Moldova f, República f da Moldávia f (formal)
11. Romanian: Republica Moldoveneasca (formal)
12. Russian: Молдавия, Молдавская Республика (formal), Республика Молдова (formal)
13. Spanish: Moldavia f
14. Swedish: Moldavien
15. Turkish: Moldova Cumhuriyeti (formal)

Origin of name: 

from Molda River (not to be confused with the Moldau)

Primary subdivisions: 

Moldova is divided into 32 raioane (sing. raion: districts), three municipiu (city), one unitate teritorială autonomă (autonomous territory), and one unitatea teritorială (territorial unit).

Note: I reused HASC codes from earlier divisions of the same name and type. I can't guarantee that the area covered is exactly the same in all cases.

Postal codes: 

Moldova uses four-digit postal codes. Moldovan addresses can be identified by prefixing the postal codes with "MD-".

Further subdivisions:

According to source [1], the secondary subdivisions of Moldova were 15 municipalities, 50 cities, 66 localities in the frame of cities, 663 villages (communes), and 886 localities in the frame of villages (communes), for a total of 1,680 secondary subdivisions.

Territorial extent: 

The UN LOCODE page  for Moldova lists locations in the country, some of them with their latitudes and longitudes, some with their ISO 3166-2 codes for their subdivisions. This information can be put together to approximate the territorial extent of subdivisions.

Origins of names: 

Chişinău: Hungarian Kis-Jenö: Little Eugene, name of a fortress
Orhei: Hungarian varhely: citadel
Soroca: Theory 1: Romanian sarac: poor. Theory 2: From sroc: a feudal obligation.

Change history: 

1. 1940-08-02: Part of Bessarabia taken from Romania and merged with part of Moldavian A.S.S.R. to form Moldavian Soviet Socialist Republic, a primary subdivision of the U.S.S.R. The Bessarabian section consisted of the Romanian counties of Bălți, Cahul, Lăpușna, Orhei, Soroca, and Tighina. They became counties (judeţul; sing. judeţ) of the new unit, with the names of Lăpușna and Tighina changed to Chişinău and Bender, respectively. The part that had already been part of the U.S.S.R. became an entity called "rayons of republican subordination." That part covered much territory between the Dnieper and Bug Rivers, including all of present-day Transnistria.
2. 1940-08-26: Chişinău and Tiraspol cities split from their superordinate units (Chişinău county and R.R.S., respectively) and elevated to the status of cities of republican subordination.
3. 1940-11-11: Bălți and Bender split from their counties and elevated to cities of republican subordination.
4. 1947-10-16: Counties abolished. Sixty rayons and seven cities of republican subordination became the top-level subdivisions of Moldavian S.S.R.
5. 1952-02-01: Four districts (ocrugul, pl. ocruguri) created as groupings of rayons and cities. They were Bălţi, Cahul, Chişinău, and Tiraspol; their capitals had the same names.
6. 1953-06-15: Districts abolished. The number of rayons and cities varied from 26 to 67 between then and independence.
7. 1990-08-16: Transnistria, consisting of almost all of the Moldavian S.S.R. east of the Dniester River, declared itself separate.
8. 1991-08-27: Moldavia declared independence, renamed Moldova. It was divided into forty districts (raioane), six towns (oraşe), and four municipal councils. Source [2] shows the following list. Populations are estimates from the 1992 yearbook. International standard ISO 3166-2, dated 1998-12-15, shows Moldova divided into the fifty divisions listed here (with no distinction between cities and towns). Change Notice 2 to FIPS PUB 10-4, dated 1999-03-01, shows Moldova divided into 41 districts (the same 40 listed below, plus Gagauzia) and four cities; the six towns are not listed.

1. Note: Many districts were split between two or more counties in the 1999 reorganization. The "Later" column in this table shows the last two letters of the HASC code for the 1999 division which contains the town whose name matches this division.
2. 1995-08: Găgăuzia district (FIPS code MD23) became an autonomous territory. Previously it had been a minority area consisting approximately of the districts of Ciadîr-Lunga, Comrat, and part of Vulcaneşti, forming two disconnected areas along the southern border of Moldova with Ukraine. Its capital is Comrat (or Komrat).
3. 1998-12-30: Moldova reorganized into nine counties, one city, one autonomous territory, and Transnistria. The International Monetary Fund requested the change as a way to reduce Moldova's administrative expenses (source [6]).
4. 1999-10-22: Taraclia county split from Cahul, to accommodate a local ethnic Bulgarian majority. As a result, Moldova was divided into ten counties, one city, one autonomous territory, and one territorial unit, as shown in the following table.

1. 2003-03-18: Moldova reorganized into the divisions shown above under the Primary subdivisions heading, under Administrative-Territorial Law No. 764 XV of 2001-12-27, approved with modifications in 2003.

Other names of subdivisions: 

During the existence of the Moldavian S.S.R., the Soviet Union imposed the use of the Cyrillic alphabet for the Romanian language spoken in Moldavia. Names transliterated from Cyrillic are different from the native forms now used by Moldova, as shown in the tables above.

1. Bender: Tighina (variant)
2. Căinari: Dumbrăveni (obsolete)
3. Chişinău: Chischiniev (Italian); Kishinev (obsolete)
4. Găgăuzia: Unitate Teritorială Autonoma Găgăuzia (formal); UTAG (informal)
5. Hînceşti: Kotovsc (obsolete)
6. Ialoveni: Kutuzov (obsolete)
7. Sîngerei: Lazo (obsolete)
8. Slobozia: Slobodzia (variant)
9. Şoldăneşti: Cernenko (obsolete)
10. Ştefan Vodă: Suvorovo (obsolete)
11. Transnistria: Dniester, Pridnestrovian Moldavian Republic (PMR), Transdniestria (variant); Dubăsari (obsolete); Stîngă Nistrului (variant); Unitatea Teritorială din Stîngă Nistrului (formal); Приднестровская Молдавская Республика (formal) (Russian)

Sources: 

1. [1] Anuarul Statistic al Republicii Moldova 2003 (Statistical Yearbook 2003). Department for Statistics and Sociology of the Republic of Moldova, Chişinău, 2003.
2. [2] Anuarul Statistic al Republicii Moldova 1992. Chisinau Universitas, 1994.
3. [3] Statistica Moldovei, http://www.statistica.md/dates.php?lang=ro&ct=21 (dead link, retrieved 2005-07-30).
4. [4] Wikipedia article Moldova  (retrieved 2005-07-30).
5. [5] CUATM2000 and CUATM2003 tables were found at http://www.statistica.md/class/index1.php?pagina=item&&nivel=pr&&clas=CUATM&&versiune=CUATM2000&&viziune=CUATM2000_JUDETE and http://www.statistica.md/class/index1.php?pagina=item&&nivel=pr&&clas=CUATM&&versiune=CUATM2003&&viziune=CUATM2003_RAIOANE (both dead links, retrieved 2005-07-30).
6. [6] Deepa Khosla wrote about the 1999-06 reorganization at http://www.bsos.umd.edu/cidcm/mar/molgaga.htm (dead link, retrieved 2000-12-21). He cites a Tass report dated 1999-02-22.
7. [7] 2004 census results for Transnistria (http://www.pridnestrovie.net/2004census.html, dead link, retrieved 2010-01-12).
8. [8] World Wide Historical Project  page about the Moldavian S.S.R. (in Russian, retrieved 2012-03-24).
9. [9] Map of Transnistria  (retrieved 2011-10-26).
10. [10] Thematic road map of Transnistria, http://www.pridnestrovie.net/images/maptransportation.jpg (dead link, retrieved 2010-01-12). Appears to show five regions, with Bender, Slobozya, and Tiraspol merged.