Simply put, without diversification, there is too much risk. There are many other ways to take on too much risk when investing, but the risk scale is different for each person as well, based upon certain other investment objectives as well as each individual's risk tolerance. Still, no on should ignore the need to diversify when investing, as too much money wrapped up in any one asset or asset type isn't good. 
There are many ways to look at diversification. I'm interested in individual securities, and my view of diversification has been largely based upon Jim Cramer's views. I don't watch his show any longer or keep up with his website, but I really enjoyed listening to his investment perspectives. He dedicated a portion of each show to helping viewers understand whether or not they were properly diversified.
It is necessary to understand that too much diversification can impact your rate of return in a negative way. You can't buy the whole stock market. Therefore, your need for more or less diversification in your portfolio can vary even based upon the investments you choose. When buying individual securities, you definitely want to spread your money not just across different stocks but stock sectors. I have selected 14 individual stocks to make up my portfolio, but that number can fluctuate. I typically only go with one or two spec stocks at the most. I included another source that describes in further detail why diversification is so important, and it even models some historical data for you. Additionally, there is a video that talks about the topic in further detail as well. Watch out for that volatile stock market, and protect yourself with proper diversification.