Make sure to balance the risk that fresh statistics cause undesirable changes to query plans against the risk that stale statistics can themselves cause query plans to change.
Imagine you have a bug database with a table ISSUE and a column CREATE_DATE where the values in the column increase more or less monotonically. Now, assume that there is a histogram on this column that tells Oracle that the values for this column are uniformly distributed between January 1, 2008 and September 17, 2008. This makes it possible for the optimizer to reasonably estimate the number of rows that would be returned if you were looking for all issues created last week (i.e. September 7 - 13). If the application continues to be used and the statistics are never updated, though, this histogram will be less and less accurate. So the optimizer will expect queries for "issues created last week" to be less and less accurate over time and may eventually cause Oracle to change the query plan negatively.