Even if you live in an arid climate, a home gutter system could be very important to the long-term protection and maintenance of your property. Without gutters, rainwater runs off the edges of the roof, down the walls (potentially damaging the walls of your home through weathering and rot) and can pool on the ground, either damaging the foundation or by flooding your home.
At the very least, it's going to splash mud all over the sides of your home (shortening the life of your paint) and damage vegetation in flower beds below.
When I bought my home I never noticed that the main house doesn't have a gutter system, but the garage does. After a particularly heavy storm, it dawned on me as I watched all my flower beds get pummeled by torrents of water, I seriously need gutters on the house!
Homes built or renovated these days are good at trapping air inside. This is good, because it means the building is energy efficient. The downside is that water may seep into the foundation or basement, creating condensation inside your home. Heating will help much of this evaporate, but moisture can remain. Some condensation will collect at windows and become merely annoying, but in attics and walls it can cause fungal wood-rot, resulting in costly repairs.
If you already have gutters on your home, it's important to keep them cleaned-out for all the same reasons stated above.
And, of course, having downspouts means you can also have a rain barrel!
(Image: Shine Window Care)