Do we really need rain gutters?
You don't need gutters. However, you will want to move water away from the home, as well as reduce any damaging effects of the water dropping from the roof.
Reduce damage from water
When it rains, all the water that lands on the roof will be shed off the edge of the roof.  This can be quite a bit of water, even with a small roof. If the water falls on a roof or structure below, it will cause excessive wear. If the water falls on the ground (soil, grass, concrete, etc.), it will eventually cut a line into the ground.
To mitigate this, you could install a louvered style gutter, rather than the traditional trough style gutter. This type of system allow the water and debris to fall through the gutter, but breaks up the sheet of water into smaller less damaging droplets.
The down side is, you'll be putting large amounts of water near your foundation.
Move the water away
If you're not using trough style gutters to move water away from the foundation, you're going to have to use other methods to do so.  The easiest method, is to maintain a grade that slopes away from the home.
Depending on the amount of rain in your area, you might have to be a bit more aggressive than simply grading away. In these situations, a french drain (or other draining system) may be a wise choice.
So do you need trough style gutters? No. However, you do have to mitigate the damage caused by sheets of water shedding from the roof. You'll also have to  move all that water away from the home. If you can achieve these things without a trough gutter system, then there's no reason to have trough gutters.
NOTE: This is not an endorsement of RainHandler products, they were simply the first brand of louvered gutter I found while doing a Google search.