The Bible mentions an ancient race called the nephilim, which has often been translated as " giants." Genesis states that:

There were giants in the earth in those days and also after that, when the sons of God came in unto the daughters of men and they bore children to them, the same became mighty men who were of old, men of renown. (Gen. 6:4 KJV)

Post-biblical tradition holds that King Nimrod was a member of this race.

The Anakites, who " come from the Nephilim" (Numbers 13:28-33), the Emites (Deuteronomy 2:10), and the Rephaites (Joshua 12:4) were giants living in the Promised Land. The Bible also records the famous strife between David and the giant Goliath, ending with the defeat of the latter. Goliath was " six cubits and a span" in height--over nine feet tall (1 Samuel 17:4).

Gog and Magog are usually considered to be giants, and are also found in the folklore of Britain.

In Greek mythology the gigantes (γίγαντες) were (according to the poet Hesiod) the children of Uranos (Ουρανός) and Gaea (Γαία) (The Heaven and the Earth). They were involved in a conflict with the Olympian gods called the Gigantomachy (Γιγαντομαχία), which was eventually settled when the hero Heracles decided to help the Olympians. The Greeks believed some of them, like Enceladus, to lay buried from that time under the earth, and that their tormented quivers resulted in earthquakes and volcanic eruptions. Greek mythology also features the cyclopes (κύκλωπες) —well remembered for their encounter with Odysseus in Homer's Odyssey—giants (though not gigantes) with only one eye. The titans were as well often imagined to be of great size and strength, whence the word titanic.

Herodotus in Book 1, Chapter 68, describes how the Spartans uncovered in Tegea the body of Orestes which was seven cubits long (3,2 meters). In his book The Comparison of Romulus with Theseus Plutarch describes how the Athenians uncovered the body of Theseus, which was of more than ordinary size. The kneecaps of Ajax were exactly the size of a discus for the boy's pentathlon," wrote Pausanias. A boy's discus was about twelve cm in diameter.

In Germanic mythologies – of which Norse mythology, due to its extensive Icelandic sources, is the only one well recorded – the giants (jö tnar in Old Norse, a cognate with ettin and ent) are often opposed to the gods. They come in different classes, such as frost giants (hrí mþ ursar) fire giants (eldjö tnar) and mountain giants (bergrisar). The giants are the origin of most of the monsters in Norse mythology (e.g. the Fenrisulfr), and in the eventual, apocalyptic battle of Ragnarö k the giants will storm Asgard, the home of the gods in Heaven, and defeat them in war, thus bringing about the end of the world. Even so, the gods are themselves related to the giants by many marriages, and there are giants such as Æ gir, Mí mir and Skað i, who bear little difference in status to them. Norse mythology also holds that the entire world of men was once created from the flesh of Ymir—a giant of cosmic proportions, considered cognate with Yama of Hindu mythology.

Bergrisar appears as a supporter on the coat of arms of Iceland.

In folklore from all over Europe, giants were believed to have built the remains of previous civilizations. Saxo Grammaticus, for example, argues that giants had to exist, because nothing else would explain the large walls, stone monuments, and statues that we know were the remains of Roman construction. Similarly, the Old English poem Seafarer speaks of the high stone walls that were the work of giants. Giants provided the least complicated explanation for such artifacts.

In Basque mythology, giants appear as jentilak and mairuak (Moors), and were said to have raised the dolmens and menhirs. After Christianization, they were driven away, and the only remaining one is Olentzero, a coalmaker that brings gifts on Christmas Eve.

Tales of combat with giants were a common feature in the folklore of Wales and Ireland. From here, giants got into Breton and Arthurian romances, and from this source they spread into the heroic tales of Torquato Tasso, Ludovico Ariosto, and their follower Edmund Spenser. The giant Despair appears in John Bunyan's Pilgrim's Progress.

Giants figure in a great many fairy tales and folklore stories, such as Jack and the Beanstalk and Paul Bunyan. Ogres and trolls are humanoid creatures, sometimes of gigantic stature, that occur in various sorts of European folklore. An example of another folklore giant is Rü bezahl, a kind giant in German folklore who lived in the Giant Mountains (nowadays on the Czech-Polish border).

Source:   Wikipedia.org