Don gave you most of the details above, but here's my two cents from doing really nitty-gritty stateful programs like system daemons in Haskell.
In the end, you live in a monad transformer stack. At the bottom is IO. Above that, every major module (in the abstract sense, not the module-in-a-file sense) maps its necessary state into a layer in that stack. So if you have your database connection code hidden in a module, you write it all to be over a type MonadReader Connection m => ... -> m ... and then your database functions can always get their connection without functions from other modules having to be aware of its existence. You might end up with one layer carrying your database connection, another your configuration, a third your various semaphores and mvars for the resolution of parallelism and synchronization, another your log file handles, etc.
Figure out your error handling first. The greatest weakness at the moment for Haskell in larger systems is the plethora of error handling methods, including lousy ones like Maybe (which is wrong because you can't return any information on what went wrong; always use Either instead of Maybe unless you really just mean missing values). Figure out how you're going to do it first, and set up adapters from the various error handling mechanisms your libraries and other code uses into your final one. This will save you a world of grief later.
Addendum (extracted from comments; thanks to Lii & liminalisht) —
more discussion about different ways to slice a large program into monads in a stack:
Ben Kolera gives a great practical intro to this topic, and Brian Hurt discusses solutions to the problem of lifting monadic actions into your custom monad. George Wilson shows how to use mtl to write code that works with any monad that implements the required typeclasses, rather than your custom monad kind. Carlo Hamalainen has written some short, useful notes summarizing George's talk.
