Greek and Latin
Ancient Greek had the word "drakon", which means "serpent."  In addition, this term are related to others which mean things along the lines of "sharp-sighted,"  "to watch,"  or "to look at."  Therefore, this creature wasn't necessarily seen as a Western Dragon as most think of it.
As a matter of fact, the Greek dragons were mainly serpent in shape. For instance, Python and Boa were both serpent-shaped dragons.
Latin had perhaps the more-well known word "draco." This, too, is translated to mean "serpent."5 The Romans saw dragons as winged serpents; however, since much of Greek and Roman mythology is related, it is hard to differentiate between Greek dragons and Roman dragons. Still, they share the common attributes as a serpent-like creature, usually with wings.
In Norse, the word "ormr" is translated to mean dragon. However, it actually means something more along the lines of "worm" or "vurm."  It is translated into "dragon" because it is used for creatures which are dragon-like or serpentine. 
The reason for the word not quite meaning "dragon" can be found in the dragons of the Norse. Jormungand, perhaps the most famous Norse dragon, was simple a huge serpent. Nidhogg, one of the only creatures referred to as a dragon in Norse mythology, was also described to be serpent-like.
The British Isles
In Ireland, the word "drag" meant fire.  This is a very interesting word to relate to the dragons of Ireland, as many of them were more closely connected with water. For instance, Muirdris was a huge water serpent; there is no mention of him being able to breath fire.
It is also interesting to note that, in Welsh, the word "dreigiaw" meant "silent meteors."  In a way, the connection between these two words suggests that dragons were seen as a destructive force; however, Y Ddraig Goch was used for the flag because of its symbol of authority.
- Nigg Wonder Beasts
- Rose Giants, Monsters, & Dragons
- Allardice Myths, Gods And Fantasy
- Wales (United Kingdom) <http://fotw.vexillum.com/flags/gb-wales.html>
For more information on footnotes and references, please see the bibliography.