It’s useful for passing to higher-order functions when you don’t need all their flexibility. For example, the monadic sequence operator >> can be defined in terms of the monadic bind operator as
x >> y = x >>= const y
It’s somewhat neater than using a lambda
x >> y = x >>= \_ -> y
and you can even use it point-free
(>>) = (. const) . (>>=)
although I don’t particularly recommend that in this case.