Oṃ is the seed syllable par excellence in Upanishadic Hinduism or Vedanta. It is the first such syllable to gain a greater significance. Oṃ is analysed into a + u + ṃ which may be why it is sometimes written as auṃ although technically I believe this is incorrect. The three aspects are said to represent, amongst other things, the Hindu trinity in their aspects as creator (Brahma), sustainer (Vishnu), and destroyer (Śiva).
Oṃ was supplanted by 'a' in Buddhism as the most important seed syllable. However it still plays an important role in mantras, most of which begin with oṃ. According to Lama Govinda oṃ presents Buddhahood in potential, and is contrasted with hūṃ which represents Buddhahood made manifest.
Although Tibetan exegesis gives oṃ a variety of different associations and significations, the main function of oṃ in Buddhist mantras seems to be to mark what follows as a mantra.
Other bījas: a | āḥ | dhīḥ | hrīḥ | hūṃ | maiṃ | tāṃ | traṃ | phaṭ | svāhā |
Examples
oṃ
Siddhaṃ
oṃ
Lantsa
auṃ
Lantsa
oṃ
Uchen
oṃ
Ume
oṃ
Uchen cursive
oṃ
Devanāgarī
auṃ
Devanāgarī
These two characters are attempts to make oṃ look like a Chinese (Seal script) or Korean character.
The oṃ on the left is based on an image in a British Museum book called Buddhism : Art and Faith, which is no longer in-print but is easily available second hand.
On the right is an oṃ inspired by an image from a Korean temple on Parhessiastes' Flickr site

This Oṃ was brushed with a flat 30mm brush (by Pro Arte) using black calligraphy ink. Using a brush one can begin to get a more spontaneous feel when writing characters. Notice the flared edges of this Oṃ which give a suggestion of movement, dynamism, or even of fire.

The similarities of Tibetan oṃ with the Siddhāṃ are not as obvious as with some of the other syllables. Its origins as a modified 'a' is visible - the Tibetans indicate a stand-alone i, o, and u by modifying the a character.