When a company goes public (i.e., issues shares to people like you and me and it starts trading on one of the exchanges) it is issued a short and unique identifier by that exchange. So, for example, the ticker for the Ford Motor Company is F, and the ticker for Microsoft is MSFT. 

What makes things interesting though is that the ticker symbol is not guaranteed to be a permanent one. Ticker symbols can change because a company moved from one exchange to another (such as from NYSE to AMEX or vice-versa), tickers can change because a company just wants to change it (such as Sun Microsystems, that recently changed from SUNW to JAVA), or even worse, ticker symbols in NASDAQ change daily because a company is late filing a quarterly report, or because it has entered bankruptcy proceedings.

At least though the US exchanges have come up with a scheme that avoids having the same ticker symbol being used by more than one exchange. So, NYSE stocks have a length of one to three letters, AMEX has two or three and NASDAQ has 4 or 5.  (In July 2007, the SEC approved a plan to allow companies moving from the New York Stock Exchange to the Nasdaq to retain their three letter symbols. See Reuters article.)

Any NASDAQ ticker symbols that have a fifth letter have a special meaning. Here is a short description for the fifth letter:

• A - Class A
• B - Class B
• C - Issuer qualifications exceptions (The letter "C" as a fifth character in a security symbol, indicates that the issuer has been granted a continuance in NASDAQ under an exception to the qualification standards for a limited period.)
• D - New issue of an existing stock (usually when a reverse split took place)
• E - Delinquent in required filings with the SEC
• F - Foreign
• G - First convertible bond
• H - Second convertible bond, same company
• I - Third convertible bond, same company
• J - Voting
• K - Nonvoting
• L - Miscellaneous situations, such as depositary receipts, stubs, additional warrants, and units
• M - Fourth preferred, same company
• N - Third preferred, same company
• O - Second preferred, same company
• P - First preferred, same company
• Q - Bankruptcy Proceedings
• R - Rights
• S - Shares of beneficial interest
• T - With warrants or with rights
• U - Units
• V - When-issued and when distributed
• W - Warrants
• X - Mutual Funds
  
• Y- ADR (American Depositary Receipt)
• Z - Miscellaneous situations such as depositary receipts, stubs, additional warrants, and units.

Although ticker symbols existed from the  time  of the  telegrams (the ticker tape  was nothing more than a continuous telegram), in the 1960s CUSIPs where introduced. CUSIP codes are 9 digit numeric codes that uniquely identify the issuer and the issue. CUSIPs are not used widely by the public, for one, because they are hard to memorize, and two, because access to the CUSIP database costs thousands of dollars. Any criticism aside, the CUSIP system is a major part of the strong infrastructure that allowed the US financial markets to grow to an enormous size.

Finally, we should mention that some indices, such as the Dow Jones Industrials, have "tickers" assigned to them so they can be broadcasted via the same systems that carry stock prices, but they do not trade.( ETFs are special funds that mirror the performance of an index but those have their own ticker symbol, just like any stock or mutual fund).