There is no ideal number of stocks you should own. There are several factors you should consider though.
First, how actively do you want to manage your portfolio. If you want to be very active then the number of stocks you own should be based on the amount of time you have to research the company, by reading SEC filings and listening to conference calls, so you are not surprised when the company reports every quarter. If you don't want to be very active, then you are better off buying solid companies that have a good reputation and good history of performance.
Second, you should decide how much risk you are willing to take. If you have $10,000 that you can afford to lose, then you can put your money into more risky stocks or into fewer stocks, which could potentially have a higher return. If you want your $10,000 grow (or lose) with the market, better off, again, going with the good rep and history stocks or a variety of stocks.
Third, this goes along with your risk to some extent, but you should consider if you are looking for short term or long term gains? If you are looking to put your money in the market for the short term, you will probably be looking at fewer stocks with more money in each. If you are looking for long term, you will be around 5 stocks that you swap as they reach goals you set out for each stock.
In my opinion, and I am not a financial expert, I like to stay at around 5 companies, mostly for the fact that it is about the ideal number of companies to keep track of.