Liquidity. Some companies believe that their stock should be inexpensive so more people can buy it. This creates a condition where more of the company's stock is bought and sold (this is called "increased liquidity"). The problem, in theory, is that the increased activity will also leads to bigger gains and drops in the stock, making it more volatile.
Many investors believe splits are a good thing. (Their thinking goes "Well, if the stock was at $15, and now it's at $7.50, it has to go back up to where it was!) This is wrong. The stock is where it was... remember that each share now represents half of the equity in the company that it did before the split. That means that each share is entitled to half the dividend, half the earnings, and half of the assets that it once was.
A few corporations have been famous for their no-split policies. The Washington Post has traded well into the $600 per share range, and Berkshire Hathaway, which was at $8 a share in the 1960's, has traded as high as $150,000. This has created the welcome condition of a stable shareholder base.