In J.R.R. Tolkien's fictional universe of Arda, Middle-earth generally corresponds to Europe. Roughly, the Shire and Imladris are positioned at about the latitude of Oxford, England, Great Britain. Therefore the Old Forest and Bree are positioned roughly about the south-east of England, possibly Norfolk, although this is unconfirmed. While the Professor had granted this exact detail, as well as often stating that the Shire intentionally resembled rural England, most the geography only vaguely matches up with actual Europe, and there are many elements that, while having analogues in the actual historical and cultural landscape of Europe, do not precisely match.
Starting in the northwest, Lindon corresponds to the remnants of Celtic Europe; and like Celtic Europe (Ireland, Man, Scotland, Wales, Cornwall, and Brittany) it is populated by a peoples who were once more populous and widespread than they are now, and have been relegated to the furthest reaches of their respective continents.
Eriador is curious, because it shows simultaneous elements of many periods in the history of Great Britain, the area which it is most analogous to. The Shire is, naturally, medieval and early modern England (one can gather this especially by the Shire Reckoning, which according to them places the end of the Third Age in the 15th century). The native peoples of Eriador (of which the Bree-folk are remnants) resemble the Celtic natives of Great Britain from before, during, and after the Roman occupation. The greatest evidence for this is the physical description of Breelanders (dark hair, stout) and place-names, which the Professor lifted from Brythonic ('bre', meaning "hill"; 'cwm', meaning "valley"; and 'chet' meaning "wood, forest"). The Romans themselves are the Numenoreans, and the fragmentation and fall of Arnor is very similar to the Roman evacuation of Britain at the start of the 5th century.
The Misty Mountains do not readily conform to anything found in Europe; however aesthetically they are extremely similar to the Alps.
Continuing east into Rhovanion one comes to Germanic Europe. In the North there is the Bardings, Beornings, and other Northmen, whose language is Scandinavian and most of whom have names lifted from the mythology of ancient Scandinavia (Gimli, Gandalf, Bard, Beorn, Dale, etc.). Moving south through Mirkwood one comes to the princes of Rhovanion who aided Gondor in its wars against the East. These have names largely of Gothic origin, who lived in many of the wooded plains of eastern Europe during the Migration Period. Lastly we come to the Rohirrim, who despite living in the wrong place geographically, are culturally and linguistically most similar to the ancient English who settled in Britain. Like the ancient English (and the ancient Germans, when they settled southern Germany) they adopted a new home in a land largely populated by Romano-Celts (Dunlendings, under the de jure authority of Gondor) after the collapse or reduction of Roman authority (depopulation in the case of Calenardhon). The works left there, such as Helm's Deep, are beyond the skill of the Rohirrim to match, but they live among them and utilize them (as the aqueducts, baths, and cities of the Romans were beyond the ability of the ancient English and Germans).
The Anduin is very similar to the Danube, despite the reversal in orientation, due to its prodigious length and its largely flat and meandering course, surrounded chiefly by woodland and occasional hills. The White Mountains do not exactly conform to the Alps, but like the Misty Mountains are most similar to them, as well as the Dinaric Alps and the Carpathians.
In the South there is Gondor, which is most akin to Byzantine Greece. Both are ruled from "new" cities (Minas Tirith and Constantinople) who are named for older places (Minas Tirith for Minas Tirith (First Age); Constantinople for Rome, as its true name was 'Nova Roma'). Both are remnants of a once-greater civilization, who suffer from both prolonged pressures from the outside, chiefly the east; as well as internal strife and plague. Indeed the two are so similar that the Siege of Minas Tirith practically plays out as a 'what-if' of the Fall of Constantinople in 1453.
Mordor falls into the area of Anatolia, Cilicia, and Armenia. Like the Ottomans and the ancient Persians, Sauron creates an empire in this area that encompasses many disparate peoples, which he uses to wage war against the West.
Harad is a conglomeration of North Africa and the Levant. Both have been either ruled by, cooperative with, or antagonistic against their respective Wests at various times, and both are geographically in the same place. The use of elephants in war was also a common feature of North Africa in Antiquity, which fits with the Haradric habit of utilizing Mumakil. This further places Far Harad with Sub-Saharan Africa, which explains the black troll-men seen at the Siege of Minas Tirith.
Rhûn is a slight conglomeration. Geographically it resembles the Volga river basin and the steppes of Central Asia. The cultures of the eastern peoples do not perfectly fit, due to the Professor only providing vague extrapolations, but the nomadic habits of many of these peoples (the Balcoth and the Wainriders) fits with many cultures who were indigenous to the Volga region throughout history (the Scythians, the Bulgars, the Turks, etc.). One of the named peoples, the Variags, derived their name from varyag, the Slavic name for Norse adventurers and traders who traveled throughout Eastern Europe and Central Asia around the 10th to the 12th centuries.