Many fantasy leagues are renewed every year on the same website. Most of the time this is done by groups of friends who play consistently rather than online leagues with random people.
Fantasy websites will archive the information from previous years so that you can look back on it and either reminisce on your victories or feel the pain of your losses.
Most information regarding the history of the league is available to see, however each website has their differences.
The typical site will have previous year's standings and playoff brackets, including the scores of the regular and postseason games. You are also able to see every transaction, meaning teams additions, drops, and trades throughout the year. Lastly, you usually have the ability to see the draft results for each year.
Yahoo fantasy has special features for past years. Players can earn trophies based on large point weeks and smallest margin of victory. Yahoo also gives out player ratings based on your year by year performance.
While it is uncommon, hardcore fantasy players could look at past years to study draft strategies and what worked out for each team. They could also see if they tended to start and sit the right people every week. Most likely, however, owners use the archive for recalling previous year's fun and for eternal bragging rights.