Gutters also keep water away from the facia and siding. This keeps them from staining and rotting.

Sometimes gutters and dry wells are required by law in order to reduce erosion and/or contamination of wet lands and waterfronts.

Gutters also avoid the discoloration and paint peeling caused by excessive splash back on modern houses (especially if slab-on-grade) where finish siding is placed so close to the ground. Adding planting reduces splash back but keeps the siding damp so it deteriorates faster.

We don't have gutters on the house at all. House is on a hill, so water flows away from house (crawl space). We do have gutter on one side of the garage, it's on the side that has sidewalk and got quite icy on the walk last year. So far, this year the gutter has made a big difference. Gutters can cause ice dams under the roof shingles and up here in the frozen north (Michigan) you don't want to mess with ice dams!
Kathy G in MI

In the long term gutters keep your house dryer because they prevent water (moisture and humidity) from seeping back in through your foundation or basement. This is almost imperceptible, initially, for most people. Usually it means it keeps your house healthier. Lowering relative humidity is a big step in the right direction, in most situations.

-david

I designed a house for my brother-in-law and he insisted that there be no gutters. I had dinner at his house on Christmas eve and when entering and leaving the house I had to walk through a curtain of water coming off the roof from melting snow (it wasn't raining). At the very least there should be "Yankee gutters" at the doors (a strip of copper formed in an "L" and inserted under the second course of shingles, sloping downward one shingle course so water is diverted enough to avoid dripping on entry paths).

Gutters should not cause ice dams if they are positioned correctly (lower than the projected plane of the roof) and the eaves are protected with self-adhering flashing. However, in a severe freeze-thaw cycle, the downspouts can be a problem.

When we remodeled we had the rotten gutters removed. The only one we replaced is over the front porch so we can walk out during the rain and stay dry. For the rest of the house we have either thick mulch (several inches) or plants that break the fall of the water.

I had RainHandler "gutters" at one time. They were great. The water falls a few inches, hits the blades on the RainHandler and turns into a mist that sprays out away from the house. There is no place for leaves to collect on RainHandler's either.