One of the most common misconceptions is that Germanic art was copied from Celtic art, although Germanic and Celtic art do look very much alike and may have influenced eachother in the border areas their art styles are too diverse and too highly developed to be "copied" from eachother just like that.
It is true however, that the contacts between the Germans and the Celts almost certainly resulted in some cultural blending in the border areas, some good examples of that can be found in my country the Netherlands where the Germanic tribes used lots of Celtic tools and jewellry that they probably traded for their own products, they even used Celtic money in some places.
Both the Germanic and Celtic cultures were descendants of Indo-European cultures which would explain the similarities in both their art and their culture.
It is also believed that Germanic art has been developed out of Asian steppe art, this is a bit exaggerated though it is true that Germanic art contains much influences from steppe art and it may be possible that the eastern Germanic tribes took over some art styles of the nomads they encountered in eastern Europe.
Although Germanic art had taken over many influences from surrounding cultures most of the Germanic art styles have probably been derived from the Pre-Germanic cultures of northern Europe, which would also explain the similarities between Germanic art and the art of its predecessors.

Germanic art is characterized by swirling and intertwined patterns, curles, plaited loops or snakes, lines and framework, wood and ivory carvings, decorated ornaments, animal figures, geometrical figures, spirals, etc. most of the known examples were found on furniture, weapons, jewellry, rock drawings, and even on gravestones.
The Germanic art styles were used by all tribes though there were also regional differences, after the 6th century abstract animal figures were introduced that were especially used by the Anglo-Saxons and the Scandinavians, some good examples can be found on Viking ships that are often decorated with beautiful snakes and dragons.
Other very interesting examples of Germanic art are Scandinavian jewellry cases, they were often made of wood or even ivory and then decorated with mythological figures, a good example is the Franks casket; it was made of whalebone by Scandinavian craftsmen in Northumbria (England) in the 7th century AD and is decorated with runes and scenes from Germanic mythology, Classical mythology, and Christian mythology.
Like most aspects of Germanic culture their art was very practical; most examples of Germanic art can be found on every day items like hairpins, jewellry, weapons, doorposts, belt buckles, etc.

Remnants of the old art styles:
Most of our current art styles have been developed in later times or are mixtures of multiple influences, but the traditional Germanic art has not entirely disappeared and its influences can still be seen in our modern art, especially the so called folk-art still has many similarities with the old Germanic art styles; folk-art is a modern form of art that is often created by amateurs and does not necessarily have to be created by professional artists, it is connected to the customs and traditions of the countryside and is often created by the people themselves as a decoration of the home, furniture, window shutters, etc.
Examples of folk-art are a farmer who decorates his wagon with flowers and fruits or a carving of an ear of corn in the back rest of a chair, carvings in boxes and cupboards often contain very old motives like sunwheels, suncrosses, rosettes, swirling patterns, spirals, world-trees, etc, though the original meaning of this symbols is nowadays unknown to most people.
Folk-art is very old and has preserved many ancient symbols and patterns of heathen origin, in later times many Christian symbols have also been mixed through it but the original character of the style can still be seen, nowadays traditional folk-art is near extinction in most countries, except in Scandinavia and the Alps where it is still widely practiced, during my holiday in Austria I have seen the most beautiful examples of it.

Examples of Germanic art:
Art from the Aspeberget rock

A Bronze Age drawing on the Aspeberget rock in Bohuslän, Sweden.
Although this art is Pre-Germanic you can already see aspects that also occur in the later Germanic art.
It depicts a hunting scene and a fleet of ships, this art form is related to the earliest known human drawings on caves and rocks, another good example of this style are the Cro-Magnon rock paintings in Lascaux, France.
The original meaning of rock art was probably religious; the people tried to "capture" the animals on the rock so they could enchant them to gain a positive outcome of the upcoming hunting, the paintings were probably also connected to fertility rituals.

Art from the Aspeberget rock

Another drawing from the Aspeberget rock, here you can clearly see the similarities between the early northern European ship designs and their later Germanic counterparts used by the Vikings, the drawing probably depicts a fishing scene.
Notice the use of the Suncross symbol, this was probably done to ensure the amount of fish throughout the year, the "target" symbol in the middle is probably a representation of the sun.


Another Scandinavian rock drawing with ships, stars, a suncross, animals, and human figures.

The Kaarstad runestone

The Kaarstad runestone from Norway, with ships and a Sunwheel symbol.

Art from the Gallehus horn

Depiction on one of the golden horns of Gallehus, Denmark; it shows warriors, animals, star symbols, and a runic inscription saying "Ek Hlewagastiz holtijaz horna tawido", historians still don't agree about the exact translation but in my opinion it means something like: "I, Hlewagastiz (=personal name) hold (this) horn (that i) made."

Martebo stone from Gotland, Sweden

The Martebo stone from the Swedish island of Gotland in the Baltic sea, some beautiful stones have been found there that show spirals, animal figures, and "Celtic style" Triskelions, this one shows a Sunwheel with a cross in the middle.

The Sundby stone from Sweden

The Sundby stone from Sweden is a good example of typical Germanic art, it is dominated by swirling and intertwined patterns and shows abstract animal figures that represent dragons or snakes.

Idol of the god Thor

This beautiful idol has been found in Iceland, it dates from around 1000 AD and it depicts the god Thor holding his hammer Mjöllnir, at weddings a hammer was held between the knees of the bride as a fertility symbol, notice that the hammer looks a bit like a cross which clearly shows the growing Christian influences in Iceland in that time.

Scandinavian brooch 7th century AD

This brooch was made in Scandinavia in the 7th century AD and depicts an intertwined snake, snakes were often used in Germanic art because they had a symbolical meaning, in almost every ancient culture snakes played an important role in mythology, the most famous snake in Germanic mythology was Jormungandr; one of the three evil demons who were the children of Loki and Angrboda, Jormungandr (also known as the Midgard serpent) lived in the sea where he sank ships and killed sailors.

Woodcarving 12th century AD

Wood carving on a door in Sweden, 12th century AD; the heroe Sigurd (Siegfried) and Regin the smith are forging Sigurd's sword Gram (also known as Balmung) with which he will kill Fafnir the dragon.

Franconian brooch

Franconian brooch made during the Merovingian dynasty in the early Middle Ages, the holes may have once contained gems.

Ostrogothic belt buckle

Silver belt buckle inlayed with enamel found in northern Italy, it was left there by the Ostrogoths.
The eagle was the symbol of the Goths who probably copied it from Asian peoples after invading the Ukraine and the Crimea.

Langobardian Iron Crown

The Iron Crown worn by the Langobardian kings, the crown was created around an iron band that was believed to be made of the nails of the cross of Jesus Christ.

Langobardian crown

Golden crown of the Langobardian queen Teodelinda.

Langobardian silver chickens

Silver chickens from the treasure of the Langobardian queen Teodelinda, 6th century AD.

Scandinavian necklace 10th century AD

Scandinavian necklace made of glass and rock crystal from the 10th century AD, the beads were created and decorated individually.
Germanic women often wore beautiful necklaces and their jewellry was very popular among Roman women.

Ostrogothic fibula

Ostrogothic fibula from the 6th century AD, made of gold and inlayed with enamel, garnet and emerald.

Franconian fibula

Franconian fibula from the 6th century AD, made of gold and inlayed with gems.

Alemannian fibula

Alemannian fibula from the 7th century AD, made of gold and inlayed with gems.

Langobardian fibula

Langobardian fibula from the 7th century AD, made of gold and inlayed with gems.

Anglo-Saxon bracteate

Anglo-Saxon bracteate from end of the 7th century or the beginning of the 8th century AD, made of gold and found in Canterbury, England.

The Franks casket

The Franks casket, made of whalebone by Scandinavian craftsmen in Northumbria (England) in the 7th century AD.

Golden belt buckle

Reconstruction of a beautiful Anglo-Saxon belt buckle made of gold from the Sutton Hoo ship burial which clearly demonstrates the skilfullness of the Germanic smiths; does this look like the work of "undeveloped barbarians"?