Fame is desired by most people at some point or points in their life, whether as a rock or movie star or someone else in the public eye. Increased fascination with these people - often termed the 'cult of celebrity', has lead to both a stronger yearning in those who are not famous to acquire fame, and a greater dislike of fame for those who have it.
Most people would like to meet someone who is famous. Beauty is of course a prime reason behind this, because a lot of celebrities are very attractive - often a major factor (if not the main factor) in them becoming famous - but glamour is also attractive. The general public dream of experiencing the kind of lifestyle, having the kind of money, possessions and contacts, and doing the types of things enjoyed by celebrities.
The other side of the coin
Experienced celebrities*, harrassed by paparazzi and everyday people, speak of the price of fame - the loss of anonymity, of privacy; the way people seem to think that they have a right to know certain things about people in the public eye. It must be tiring and even frightening to be followed, stopped, questioned by total strangers who know the tiniest details about you.
So celebs hate being famous, right?
And yet they don't chuck in their fame. Because despite all the inconvenience and sacrifice, they decide that they still want to live that sort of life. Some treasure privacy more than others, but an awful amount of them went into their respective industries to gain public recognition for their abilities;
Fame will always attract people. The amounts of money involved, the interest people take in you, the lifestyle...of course fame is attractive. Wouldn't you like to have financial security*? To mix with some of the best-looking, most dynamic and successful people around? Wouldn't you like people to wish they knew you - or were you? To be adored by millions?