To me a more general way is via a monad/comonad pair. This generalizes the common "monad" approach which should correctly be called the "strong monad" approach, since it only works with strong monads.
Moving to a monad/comonad pair allows effects to be modeled that result in some variables no longer being available. An example where this is useful is the effect of migrating a thread to another host in a distributed setting.
An additional method of historical interest is to make the whole program a function mapping a stream/list of input events to a stream/list of output events. See: "How to Declare an Imperative" by Phil Wadler: http://www.cs.bell-labs.com/~wadler/topics/monads.html#monadsdeclare