American Gold Eagles, because they are minted in four sizes and denominations, are often collected in four-coin and other sets. Some people like to assemble their own, or purchase from a coin seller, a full set of each year's business strike bullion coins, often in professionally-graded form. Others like to acquire the 4-coin proof sets either in original government packaging, or in a set of graded and encapsulated coins, especially in the top grade of proof 70.
In addition, the U.S. Mint has also issued some special anniversary American Gold Eagle sets for collectors. These include in particular the popular 2006 20th Anniversary set of three 1 oz. coins, which had a mintage limit of just 10,000 coins and sold out quickly. That set included the first and only reverse proof Gold Eagle plus a 2006-W burnished coin and 2006-W proof coin.
Then there is the 1995 10th Anniversary 5-coin set, which included a 4-coin set of that year's proof Gold Eagles struck at the West Point Mint plus the key-date 1995-W proof Silver Eagle, which has emerged over the years as a very valuable coin and the lowest mintage coin in that series.