According to a Reuters article by Helen Kearney, Fidelity Investments recently surveyed over one thousand millionaires and asked them, "How much money do you need to have to be truly rich?" The millionaires, whose average investments hover at around $3.5 million, answered that they would need at least $7.5 million to actually be rich. The main issues concerning one's perception of how rich you are involve your peer group (how rich am I compared to my friends) and whether or not your money can support your lifestyle until you die. If you read the article, be sure to pay attention to the percentage of the millionaires who do not consider themselves wealthy.
You can read the Reuter's article here.