The S&P 500 index dates back to 1957 in its modern version (although it has been extrapolated backwards to several decades earlier for performance comparison purposes). This index provides a broad snapshot of the overall US equity market; in fact, over 70% of all U.S. equity is tracked by the S&P 500. The index selects its companies based upon their market size, liquidity, and sector. Most of the companies in the index are solid mid cap or large cap corporations. Like the Nasdaq Composite, the S&P 500 is a market-weighted index, so it provides a fair assessment of the stocks that it tracks. Most experts agree that the S&P 500 is one of the best benchmarks available to judge the market. Its only possible fault is that it does not include foreign stocks (except for a handful that have traditionally been included).
If you're looking for an index that captures the state of the entire market, you need look no further than the Wilshire 5000. Founded in 1974 by Wilshire Associates, the Wilshire originally listed 5,000 stocks, although in subsequent decades it grew to include considerably more. The Wilshire now tracks over 7,000 stocks (although the name kept the 5,000 number in it for consistency). The index tracks every stock for every company that is headquartered in the United States, leading some to call it the Total Stock Market Index. Like the S&P 500 and the Nasdaq, the Wilshire 5000 index is a market capitalization-weighted index.
The Russell 2000 index is used to track the performance of 2,000 small-cap stocks. These aren't necessarily the smallest 2,000 companies in existence; instead the index is composed of the 2,000 smallest companies in another related index, the Russell 3000, which tracks the 3,000 largest companies in the U.S. So in that sense the Russell 2000 can be thought of as the "smallest of the large companies." Even so, the Russell is a well-diversified index of small-cap stocks that is a useful benchmark for those interested in only small companies.
In addition to all the domestic indices mentioned above, there are a number of indexes used around the world and in the U.S. that track foreign stocks. Morgan Stanley, for example, has a Europe Australasia Far East (EAFE) index that is used to track stocks in developed markets in those parts of the world. England has the FTSE 100 (pronounced "footsie"), a British equivalent for the Dow. And Japan has the Nikkei 225, another index similar to the Dow that dates back to 1949.