This answer is from an Australian perspective and applies to spoken use of the word. The other answers address the written form so I won't touch on that.
"Greetings" as a salutation might be used when addressing an individual or individuals in a formal settings, such as addressing a crowd, or a dignitary greeting people of another culture. Because most of us wouldn't find ourselves in situations where such a word is appropriate, it tends to be used ironically instead.
For example, when meeting friends out for dinner, you might say "Greetings" as a light-hearted way of introducing yourself. It's not uncommon to hear this, but I also wouldn't suggest adding this word to your daily vocabulary as it would probably come across as pretentious if you made a habit of greeting people this way.