Who else liked this character in Star Trek? For me his mind-blowing abilities, mystical background and independence made him quite irresistible. John de Lancie played him so well too. And one other thing, we probably all have some strong desires towards space. Some may see it all as a living thing even. Wouldn’t it be better to be somehow in direct contact with it, without any technology? The difference is like taking a boat trip vs. swimming inside the water, feeling it with every cell of your skin. Q had all that and more.