I just found the best cat photo for a long time:
Unfortunately, this is not a question that is likely to be solved soon. It already stood for a long time, and only a few weeks ago there was another unsuccessful attempt to prove it. Well, to be precise there are such "attempt" every week, but most of them are just attempt to get attention (and to win the one million dollar prize) by people who simply don't know math well enough to prove this theorem. The attempt I mentioned was a paper submitted by a professor who already had some previous work done about the RH. While this proof was met without much optimism, it looked serious. But even in his paper an error was found in 24 hours.
By the way, while there is a prize for proving RH, there is no prize for showing that it is wrong. In my opinion the reason for this is that showing it wrong doesn't necessary require mathematical advance. All you need to show that it is wrong is to find a zero of the Riemann zeta function which is not on the critical line. This can be done using a computer, without bringing any new ideas to math.