This is an excellent question. There are approximately 10,000 chateauxs in Bordeaux, most of them producing very ordinary wine. There is a classification of the finest chateaux. Unfortunately, the so-called 1855 Classification (which covers, with one exception, the red wines of the Medoc and the whites of Sauternes-Barsac) was created in 1855. Some question its relevance for many of the wines from chateaux not in the top tier (known as the 1st Growths). The 1855 Classification was created by marketers and reflected the sales figures for Bordeaux wines in the previous decade. Many of the top (and not-so-top) Bordeaux xhateaux have bought and sold land so the wine labeled "Chateaux Top-Growth" today may come from entirely different vines on different soil and rock in a different micro-climate, i.e. it bares only a passing resemblance to the 1855 wine. Many chateaux have disappeared having been subsumed by another nearby chateaux. You need to know your history and geography when investing in Bordeaux wines.

Here's a link to an explanation of the 1855 Classification. Please note that a couple of chateaux in the 2nd and 5th Growths would, if classified today, most probably be included wmong the 1st Growths:
http://en.wikipedia.org/wiki/Bordeaux_Wine_Official_Classification_of_1855

One bottle can cost hundreds, thousands or tens of thousands of dollars so it is a rare wine lover who has an opportunity these days to enjoy these wines. There are many excellent wines from the Medoc that are not included in the 1855 Classification.

St. Emilion in Bordeaux has its own Classification:
http://en.wikipedia.org/wiki/Classification_of_Saint-%C3%89milion_wine

So does Graves in Bordeaux:
http://en.wikipedia.org/wiki/Classification_of_Graves_wine

Any changes made to the Classifications must be approved by various bodies and the Ministry of Agriculture.

The 1st Growths of Bordeaux are:
Chateaux Lafite Rothschild
Chateaux Latour
Chateaux Margaux
Chateaux Haut-Brion
Chateaux Mouton-Rothschild

If you are planning to purchase 1st-5th Growth or other classified wines of Bordeaux please learn which years (vintages) were good to great)! Also, be aware that many people investing in such wines in recent years saw the value of these wines drop precipitously (although some are coming back up in price a bit).