Many of today's collectors started collecting U.S. postage stamps as kids, often with a parent or family member. The US stamp collecting market has weakened in recent years, however, with many stamps and even entire collections trading below face value (so many copies of common stamps were printed that there's not enough demand to warrant a premium).
Rare or unusual U.S. stamps, however, are another story - there's a robust market for those, and some specimens can be worth thousands of dollars or more.
There are many ways to approach collecting U.S. stamps. Some collectors focus on a specific time period, like the 19th century. Others choose specific themes like airmail stamps or duck stamps. Some focus on specific formats like sheets, plate blocks, coils, or booklets. There are also a large number of collectors who focus on first day covers - stamps that were affixed to a special envelope and cancelled on the first day of issue.
As with many collectibles, rarity and condition are two key determinants of value. U.S. stamps can be either unused (never cancelled) or used, and there are collectors who focus on both varieties.