Kosovo, Northern Cyprus and the Caucusus' states of Abkhazia, Nagorno-Karabakh, and South Ossetia already. Transnistria is not a member of the Caucusus region, but Transnistria's independence claims stem from the collapse of the USSR like these Caucusus would-be nations. Transnistria is sandwiched between the Ukraine and Moldova. Moldova, from whom they claimed independence, doesn't not recognize them and still holds Transnistria as part of its sovereign territory. Transnistria has a much older history though than the current independent or not state.
In prehistoric times and antiquity it was occupied Dacian and Scythian tribes, settled by Greek colonists at Tyras and eventually became a Thracian homeland to a branch of the Getae. The area would fall under the sway of the Roman Empire in 56 AD when Rome rebuilt the city of Tyras along the Black Sea. Tyras would become an important minting city for Rome and over a couple of centuries this city in what Rome called Lower Moesia. Numerous copper coins would go out from Tyras throughout the whole empire.
As the Western Roman Empire was collapsing the area would see a whole host of people groups swing through, including the Goths and the Huns. The Huns would destroy the city of Tyras but the Goths would stick around for centuries and live throughout Transnistria. Then the Slavic peoples migrated through the area, both Southern and Eastern tribes. Also various Turkic peoples would settle and then move sometimes living alongside Slavic tribes and other times displacing them. The area would eventually become dominated by a Turkic confederation by a tribe called the Cumans. Cumania, a land more or less controlled by this semi-nomadic confederation stretched from the Balkans in the west to the Caucusus and further east into modern Iran. This large swathe of land brought them into conflict with the new threat from the east, the Mongols. But the Mongols didn't establish any tangible permanent legacy and the region entered part of the Kievan Rus' sphere of influence.
At about the turn of the 15th century the area became part of the Grand Duchy of Lithuania and then part of the Lithuanian-Polish Commonwealth. This would last for nearly 300 years until the area was taken over by the Russian Empire in 1792 and 1793. By this time the area was occupied primarily ethnic Moldavian, ethnic Ukrainian and a number of various Tatar peoples (one of the few holdovers from Mongol invasions). Under Russian influence which lasted from 1793 until the Russian Revolution in 1917 the area was heavily colonized. Russian peasants were moved there to be given land (as all of the Russian land was in the hands of noble Russians). Also, Jews and Germans were moved to the region to help build up the economy.
After the fall of the Russian Empire and the dawn of the USSR, Transnistria became a part of the Socialist Republic of Moldova under the power of the Kremlin. The area was not given any rest though as it was invaded during World War II when it came under the control of Romania. Romania instituted a strict Romanianization program over the area and a multitude of Ukrainian and Moldovan Jews were either killed or sent to concentration camps by combined Romanian and German forces. Other ethnic groups were relocated and forced to move. After the war the Soviets reacquired the region but took a page out of German/Romanian playbook and relocated numerous Moldovan and Romanian families, often eastward to places like Kazakhstan and Siberia.
In the late 1980's as the USSR was coming apart at the seams the Moldovan authorities pushed for more autonomy and power. They readopted the Latin alphabet, declared Moldovan to be the only official language of the region and declared the closeness of Moldovan and Romanian linguistic heritage. This nationalism and ethnic posturing caused many Russian speaking and Slavic ethnic groups to become very uncomfortable. They were worried about two major things. First, the rhetoric of some of the Moldovan groups was very damning to non-Moldovan/Romanian people living within Moldova. Second, they were terrified by a reunification of Romania and Moldova.
In response to all of this war broke out as the people who did not want to return to a Romanian-Moldovan alliance attempted to break away from Moldova. From 1990 - 1992 war between Moldovan and Romanian forces against the breakaway region raged. Transnistria would have been easily crushed had it not been for support they received from official elements of the Russian army, Russian volunteers and Ukrainian volunteers. As a result of the war Transnistria has been a de facto state since 1992, only it has been almost entirely recognized as a part of Moldova by the international community.
Since 1992, the government of the Pridnestrovian Moldavian Republic (Transnistria) has been ruled from its capital of Tiraspol, a city built on or near the ruins of the Greek settlement of Tyras by the Russians in 1792. The population of Transnistria is over 30% Moldovan, making it the largest percentage of the population. However, ethnic Russians and Ukrainians combine for a near 60% of the population. Thus, they speak Slavic based Russian language and use the Cyrillic alphabet in Transnistria as opposed to the Romance based Moldovan language and Latin alphabet used in Moldova. Tensions still simmer in this disputed region, especially given the fact that FC Sheriff Tiraspol dominates the Moldovan Football League. In a recent BBC World Football report it was noted that crossing the border from Moldova to Transnistria for a football match was a lot like crossing the border back into the days of the USSR, murals, police checkpoints, complete with hammer & sickle and all. It is a starkly different place than both Moldova and Ukraine which border it.