This is a good question, one that may come up more often in multifaith circles. For some (but not all) Jews, it's actually a sign of respect not to write God's name in full. The concern is that the word may be written on something that will later be thrown away or otherwise destroyed. For example, you might print out a copy of an article that mentions God, but later toss it in the trash along with old coffee grounds. Not exactly a place redolent of majesty.
The website jewfaq.org explains this in more detail:
"Jews do not casually write any Name of God. ...Judaism does not prohibit writing the Name of God per se; it prohibits only erasing or defacing a Name of God. However, observant Jews avoid writing any Name of God casually because of the risk that the written Name might later be defaced, obliterated or destroyed accidentally or by one who does not know better. Normally, we avoid writing the Name by substituting letters or syllables, for example, writing "G-d" instead of "God."Though not all religions take the same tack, and may allow you to toss such printed matter, most faiths have some written way of showing respect for the sacred. For example, many Christians capitalize "His" and "Him" when they refer to God or Jesus. When Muslims write the Prophet Muhammad's name, they usually follow it with the abbreviation (pbuh), meaning "Peace be upon him."
Have a question about another religion's ceremonies and traditions? Write to firstname.lastname@example.org and include "religious etiquette" in the subject line.