Short Answer
Water can back up and overflow. It can also discharge too close to the foundation.
Detailed Explanation
Downspouts carry water from the gutters to ground level and away from the foundation. If downspouts are too few or too small, water backs up in the gutters and overflows. If downspouts discharge too close to the foundation, the water they carry saturates the soil next to the foundation — the same problem that gutters are supposed to prevent. Proper downspout design includes: adequate number and size for the roof area and gutter capacity, proper placement at low points in the gutter run, extensions or underground drainage to direct water at least several feet from the foundation, and clean, unobstructed discharge points.
Why It Matters
Gutters with inadequate downspouts can cause overflow and foundation water problems, even if the gutters themselves are properly sized.