Guttering, why exist?

[Pipbin]

We have a slightly oddly laid out house. At the back we have a 'summerhouse'. It is basically a lean-to built onto the back of the house. It has no access to the inside of the house and is below floor level, the house is built into the slope and the back of the house is a story below ground level.

Anyway, I'm planning in replacing the roof on the lean to and I've realised that the guttering goes nowhere other than to a water butt.
Do I really need guttering? It's only a small roof and the wall is not actually a wall of the house.

Without it, the wall will get very damp. I've seen horrific damp issues where there is failed guttering.

As SocksRock says - without guttering all rainwater will run down the walls and you'll get penetrating damp problems. There is a reason guttering was invented - necessity is the mother of invention after all!