The 20 stocks theory
What's the ideal number of stocks to own in a portfolio?
This question tried to be answered by Harry Markowitz in 1952 through his modern portfolio theory and fine tuned by Ben Graham in 1968 in The intelligence Investor who suggested that adequate diversification can be obtained with 10 to 30 stocks.
As shown in the following chart, please see what happens when you select stocks uncorrelated with each other like different company size, industry, sector and country :

Or through this chart made by Mornigstar:

Observations :
From the above images you noticed that to the certain extent you can get benefit of diversification but after that the effect is minimal;
Pay attention that since the "online world" that theory must be fine tuned due to the impact of taxes and transaction costs (more or less 50 stocks would be the best balance);
If you are not an expert in stocks selection ETF's, Index funds or mutual funds will be the good solution to find that diversification;
There is a big uncertainty the systemic risk, like an economic recession dragging down the entire stock market that's what Nassim Nicholas Taleb call the Black Swan "The Impact of the Highly Improbable" which is a bias of the modern portfolio theory;
Risk can never be eliminated completely;
According to Warren Buffett: "wide diversification is only required when investors do not understand what they are doing". In other words, if you diversify too much, you might not lose much, but you won't gain much either.
Sources :
Figures:

http://www.basunivesh.com/2012/09/21/is-over-diversification-impacting-your-portfolio/http://www.efficientfrontier.com/ef/900/15st.htmhttp://www.redwoodwm.com/newsletters/the-black-swan-returns-february-newsletter/