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FOOL SCHOOL
The basic argument for buying lots of shares is that you reduce your overall risk and the damage inflicted by one or two poor share selections. This is known as diversification. Of course the flip side is that if you buy too many then you don't benefit that much from your best selections either. Many investors find that a large chunk of their gains come from just one or two shares. If you buy too many shares you will also incur more in charges and this will impact upon your returns.
Groups of shares like small companies or telecoms companies tend to move en masse. Therefore they will all tend to go up or down over any given period. Naturally some will move more than others but if all your shares come from one or two sub-groups then the overall value of your portfolio is likely to be more volatile. Technology investors have found this out to their cost in the last couple of years. If you have enough confidence in your selections over the long-term then this is less of a problem. But from the beginner's point of view, and for peace of mind, it makes more sense to pick a selection of shares from different sectors.
As long as you have done this then there is probably no need to buy more than 12 individual shares. Studies have shown that buying additionial shares above this level doesn't reduce your overall risk to any significant degree. In fact many people seem to be prefer between 6 and 10 shares, if they are attempting to get market-beating returns.
Another fact to bear in mind is that you will need to keep an eye on each company. The more companies you have to follow the harder and more time consuming this becomes. As you buy more and more shares the chances are that you will get less and less selective about your choices. It's better to concentrate your firepower on a smaller number of shares that you know well and have the most confidence in.