Just like the S&P 500 can be seen as a proxy for what is happening to the equity of US companies there are indices that act as a barometer for the health of stock markets worldwide.
There are several reasons that traders keep an eye on stock markets worldwide:
1.- It can be used to gauge the interest of investors worldwide in the equity of companies in foreign markets.
2.- It is a reflection of economic prospects for the countries in question. For example, stocks in companies that operate in economies that are growing rapidly (such as the ones in the BRIC countries currently) will command higher valuations than stocks in countries where growth is moderate to sluggish or even non-existing or negative.
3.- Traders can diversify their portfolios geographically to minimize risks. This can be done investing directly in the foreign markets or from the US through ETFs that track the indices abroad. Not only will this diversify a trader's portfolio geographically but it will also diversify it in terms of currency (although this can also be seen as taking on new risk in the form of foreign currency risk).
4.- Traders can use indices in some countries (such as the ones in Asia and Europe) to gauge market sentiment for the current day, since markets open for trading in Asia and Europe earlier than in the US. For example if on the monday starting the week Japan is in sell-off mode there is a good chance that the market in the US will also start with a negative tone.
5.- Traders can also use the stock market of a foreign country as an indicator of market sentiment and use this to establish positions in the forex market (for example going long the currency of a country whose stock market has been increasing lately).
The main indices that I look at are (in approximate order of importance):
Japan: Nikkei 225
England: FTSE 100
China: Shanghai Composite
Canada: S&P TSX
France: CAC 40
Hong Kong: Hang Seng
South Korea: KOSPI