There are a few situations in which it may be advantageous to exercise early. Wikipedia actually has a good explanation:
Option Style, Difference in value
To account for the American's higher value there must be some
situations in which it is optimal to exercise the American option
before the expiration date. This can arise in several ways, such as:
An in the money (ITM) call option on a stock is often exercised just
before the stock pays a dividend that would lower its value by more
than the option's remaining time value.
A put option will usually be
exercised early if the underlying asset files for bankruptcy.
A deep ITM currency option (FX option) where the strike currency has a
lower interest rate than the currency to be received will often be
exercised early because the time value sacrificed is less valuable
than the expected depreciation of the received currency against the
An American bond option on the dirty price of a bond (such as
some convertible bonds) may be exercised immediately if ITM and a
coupon is due.
A put option on gold will be exercised early when deep
ITM, because gold tends to hold its value whereas the currency used as
the strike is often expected to lose value through inflation if the
holder waits until final maturity to exercise the option (they will
almost certainly exercise a contract deep ITM, minimizing its time