Stock Splits

A stock split simply involves a company altering the number of its shares outstanding and proportionally adjusting the share price to compensate. This in NO WAY affects the intrinsic value or past performance of your investment, if you happen to own shares that are splitting.
A typical example is a 2-for-1 stock split. A company will announce that it's splitting its stock 2-for-1 in one month. One month from that date, the company's shares (having traded the day before at, say, $30) will now be trading at half the price from the previous day (so they'll open at $15). The company, which had 10 million shares outstanding, now consequently has 20 million shares outstanding. The price has been halved in order to accomodate a doubling of the share total.
The most common splits are 3-for-2, 2-for-1, 5-for-4, and 3-for-1. But they can happen any which way: 5-1, 10-for-9, etc. They can even happen in "reverse": 1-for-10, etc.

But why the heck would a company do this?

Hey, excellent question. A few reasons. First, as a stock price skyrockets, some people will be psychologically unwilling to pay that "high price" so a stock split brings the shares down to a more "attractive" level. Again, the intrinsic value has NOT changed, but the psychological effects may help the stock. Second, a stock split generally occurs in the face of new highs for the stock. Thus, it's an event dripping with positive connotations and associations. . . it's makes bulls snort and roar to suddenly have "twice as many shares" as they started with, for example. Third, and final, with lower-priced shares, a stock's LIQUIDITY (FAQ topic, see LIQUIDITY) increases, often reducing the BID/ASK SPREAD (FAQ topic, see BID/ASK SPREAD) and making it easier to trade. This is always good.

I buy 100 shares of ABC Inc. for $10 shares. Six months later the stock is at $20 and splits. Now I own 200 shares at $10 each. However, do I also halve my base purchase price to $5---or does my original, base purchase price remain $10?

Yes. Your cost basis (ignoring commissions) is now $5/share. Not to worry! Your money can't evaporate into thin air!

What happens if you buy a stock after the "record date" for the split but before the listing change?

The "record date" means virtually nothing to the stockholder. If you bought the stock before the split, your shares will split the same day everyone else's do, regardless of the record date. You won't lose on the split.

I was wondering if I placed a stop order, then a stock splits and begins trading below the stock price, if my stop order would become a market order. I know this wouldn't make sense but I don't like to take chances.

We checked with Charles Schwab on this. Their policy is to simply cancel the standing order. They do not automatically readjust the stop price to reflect the split. The best thing to do in this case is place the order again following the split date.
They do not, of course, stop you out following the split based on your pre-split stop order. Any broker who did this would likely not be in business long. Call it survival of the fairest!