Obama is the leader of America and seems to be a particularly famous one. Lets say the entirety (or as close to it as is possible) of North America know who he is. We can probably throw in basically all of Europe as well. Australia and other Westernised countries too. Do people in South America know much about the USA? I'm not really sure, but from what little I know I'd imagine a decent portion of people in Central and South America stand a good chance of having heard of Obama.
People in the Middle East stand a decent chance of having heard of the leader of the USA, given its activities there. I'm sure plenty of Japanese people know who he is as well. As for China and India? I don't really have any idea, as I don't really know anyone who lives there so have no clue what the average citizen of those countries knows about the rest of the world. But given the pervasiveness of America in the media and the general ignorance of people in the West about other cultures, my guess is that knowledge of the USA is at least as penetrative of China and India as knowledge about those countries is penatrative of USA and other Western countries (i.e. it's unlikely the people in the west know more about Chinese and Indian culture than they know about Western culture). I don't know if there is one figure who is universally known across both India and China - if there is then there's probably a decent chance that could be the most famous person in the world. But if figures are only likely to be universally known within one or the other of those countries, I think it's unlikely they'd be the most famous person in the world - someone universally known within China but relatively unknown outside it would only be known by a billion and a half people. And given the large proportion of people in India and China living in completely rural areas, the chances of any one person so pervasively known aren't as high - especially across both countries.
I completely get that the entire world isn't America, and people in third world countries may not know anything about America, and that places like China and India may have lots of people who don't either, and they make up nearly half the world's population. And I get that my knowledge of famous people is just that of someone from the UK. But I'd still make the case that someone like Obama is very likely the most famous living person in the world. The people who have not heard of him are more likely to be people disconnected from the worldwide media, and hence are unlikely to have any single person known to all of them. And America is the biggest media-whore, so if people know anything about worldwide affairs, it's likely they'll know at least something about the USA. Hell, the most famous person in the world could theoretically be known to only a small proportion of the world population, if the rest of the people in the world don't share knowledge of any other single person.
Edit: The Pope and The Queen are decent candidates as well. For The Pope though, how many people in the world could actually tell you the current Pope's name offhand? Significantly less than people who know the title exists, I'll guess.