Many Digimon are based on some mythological creature...but sometimes, these mythologies play a bigger role within the Digimon universe. The stories of the distant pasts of many of the Digital Worlds strongly resembles that of our world...
The Four Holy Beasts
The four Holy Beasts are based on Chinese gods...however, they were eventually "brought" to Japan, where they were called Seiryuu (Blue Dragon), Genbu (Black Turtle), Suzaku (Red Sparrow), and Byakko (White Tiger). The Digimon fandom and Bandai of America, however, seem to prefer using the Chinese names - Qinglongmon (Azulongmon in the dub), Baihumon, Xuanwumon (Ebonwumon), and Zhuqiaomon.
In Japanese and Chinese mythology, Seiryuu guarded the east, Genbu the north, Suzaku the south, and Byakko the west. This was incorporated into the Digital Worlds of Digimon Adventure and Digimon Tamers: Qinglongmon protects the Eastern Hemisphere, Xuanwumon protects the Northern Hemisphere, Baihumon protects the Western Hemisphere, and Zhuqiamon protects the Southern Hemisphere. The Digimon were said to have born at the very beginning of the Digital World - although Xuanwumon is the eldest and wisest of the four, while Baihumon is the youngest and strongest of the guardians. Their existence seems tied in some manner to the Digital World, and it's possible they are the ones who shaped the Digital World.
The Twelve Olympian Gods
Marsmon, Neptunmon, Mercurimon, and Minervamon are the only current members of this group, which is based on the Twelve Olympian Gods in Roman mythology. Very little is known about this group.
The Great Angels
Currently, there are five "great angels", although only Seraphimon, Ophanimon, and Cherubimon are actually called Great Angels. In Judeo-Christian mythology, there are nine classes of angels: Seraphim, Cherubim, Ophanim (or Thrones), Dominions, Virtues, Powers, Principalities, Archangels, and Angels. In Digimon, these ranks are represented by Seraphimon, Cherubimon, Ophanimon, Dominimon, and Slash Angemon (Power). Other Digimon may represent the other ranks, but those five have names and/or types that definitely put them in those ranks. Angemon, d'Arcmon, Angewomon, and Pidmon are Digimon that probably represent the Angel rank; Holy Angemon probably represents Archangels, going by types.
The Seven Great Demon Lords
The Seven Great Demon Lords are Lucemon Falldown Mode, Belphemon, Demon, Lilithmon, Leviamon, Barbamon, and Beelzebumon. Each one is based on a legendary demon, and represents one of the Seven Deadly Sins (athough there is a slight variance in what the Digimon represent and what the actual demons represent...) On Lucemon Satan Mode, Lucemon Falldown Mode's evolution, you can see several circular shapes projecting off of his body with strange symbols on them. The LCD site created a clear image of these symbols:
Lucemon Falldown Mode represents the fallen Lucifer, the greatest of all the angels and the one who was the leader in the rebellion against God. His sin is Pride. The orange symbol on the top represents Lucemon Falldown Mode, and according to the LCD site the symbols on the "crests" represent celestial bodies used in astrology. Lucemon Falldown Mode is the Sun.
The yellow-orange symbol represents Beelzebumon, who is based upon Beelzebub. In Milton's Paradise Lost, Beelzebub is one of Lucifer's chief lieutenant. His name derives from Baal, but he is also called by a Hebrew word that means "Lord of the Flies". His sin is Gluttony, and his planet Venus.
The dark blue symbol represents Belphemon, who is based on Belphegor, a Moabite god. His sin is Sloth and his planet Mars.
The purple symbol represents Barbamon, who is based on Barbatos. His sin is Greed, although this is normally associated with Asmodeus. His planet is Saturn.
The yellow symbol represents Demon, who seems to be based upon a generic demon, although he has the Elder Sign on his cloak. The Elder Sign is a symbol in Lovecraft mythos used to protect the Elder Ones from Cthulhu. He is also said to be a fallen Seraphimon. His sin is Wrath, and his planet Jupiter.
The light blue symbol represents Leviamon, who is based upon the legendary Leviathan. The Leviathan is generally considered to be some kind of large sea creature, but in Paradise Lost he is an extremely strong demon who is one of Lucifer's chief lieutenants. His Sin is Envy and his planet Mercury.
The green symbol represents Lilithmon, who is based upon Lilith. Lilith was said the be Adam's first wife, who left him and slept with Satan. She became a female demon, who, uh, did bad things relating her sin, which is Lust. Her astrological thing is the Moon.