I know it happens, but I've never seen it once.
I'm a total stock amateur; I just invest small-scale amounts that I have to spare for the sake of experience/practice and a maybe a little fun.
But why have I never seen a stock split? They just keep going up, the ones that do well, and I never see them get reduced that way.
Are you sure you're not just looking at prices that are adjusted for the split, e.g. Yahoo? For example, Gilead Sciences (GILD) split a few months ago, but if you look at a price chart, there isn't an interruption even though the split is clearly marked. (Look in the past six months; it split in January). However, you could also simply be watching companies that happen to not split, for a variety of reasons. This isn't a criticism, but rather just a consequence of whatever stocks you happen to be watching.
However, a quick search for information on stock splits yields a few articles (mainly from the Motley Fool) that argue that fewer companies are performing stock splits in recent years; the articles mainly talk about tech companies, and they make the argument that even though the shares in Google and Apple have a high stock price:
Google and Apple aren't all that expensive by traditional valuation metrics. Google trades at just 15 times next year's projected profitability. Apple fetches a mere 13 times fiscal 2012's bottom-line estimates.
These articles are a bit dated in terms of the stock prices, but the rationale is probably still good. Similar logic could apply for other companies; for example, since May 2009, Panera's stock price has climbed by almost a factor of 4 without splitting.
The articles also make the point that stock splits were traditionally seen as bullish signs because:
Companies splitting to bring their share prices back down to more accessible levels were optimistic in building those sand castles back up.
One could make a fair argument that the overall economic climate isn't as bullish as it used to be, although I would only be convinced that this was affecting stock splits if data could be gathered and tested. A stock split can also raise the price of a stock because if small investors feel the stock is suddenly more accessible to them, they purchase more of it and might therefore drive up the price. (See the Investopedia article on stock splits for more information). Companies might not see the necessity in doing this because their stock price isn't high enough to warrant a split or because the price isn't high enough to outprice smaller investors.
One interesting point to make, however, is that even though stock splits can drive small investors to buy more of the stock, this isn't always a gain for the company because professional investors (firms, institutions, etc.) have a tendency to sell after a split. The paper is a bit old, but it's still a very neat read. It's possible that more and more companies no longer see any advantage to splitting because it might not affect their stock price in the long run, and arguably could even hurt it. Considering that large/professional investors likely hold a higher percentage of a company's shares than smaller investors, if a stock split triggers a wave of selling by the former, the increasing propensity to buy of the latter may not be enough to offset the decline in price.
Note: My answer only refers to standard stock splits; the reasons above may not apply to a decrease in the number of reverse stock splits (which may not be a phenomenon; I don't know).
You haven't seen one because you haven't looked for one properly. You can set a google alert for stock split and get information about major issues splitting their stocks quite regularly, as well as a daily dose of recommendations from people without a say in the matter for big companies to split their stock.
Stock splits are announced in advance by company management.
If you want to see one split, well, a reverse split anyway, keep an eye on TZA, FAZ, BGZ, and any Direxion fund. These funds decay continuously forever. Once they get close to $10-$15 or so, they reverse-split them back to the $30-$50 range and the process starts over. This happens about once a year.
A few years ago I sent Direxion an email asking what happens when they run out of shares to reverse split and the reply was that's its an open fund where shares can be created or redeemed at will. That still didn't answer the question of what happens when they run out of shares. If they create new shares, the price will drop below the $10 level where many fund managers aren't allowed to buy.
