Short Answer
Generally, runoff should be directed away from the foundation in an appropriate manner.
Detailed Explanation
Downspouts that discharge right next to the foundation defeat the purpose of the gutter system. The water they carry saturates the soil around the foundation, which can lead to foundation cracking, basement or crawl space water intrusion, and soil erosion. Downspouts should discharge at least 4-6 feet from the foundation, either through above-ground extensions, underground drainage pipes, or splash blocks that direct water away. In areas with heavy clay soil or poor drainage, longer extensions or underground drainage systems may be needed. The goal is to move roof runoff far enough from the foundation that it doesn't saturate the soil that supports the foundation.
Why It Matters
Downspouts that discharge near the foundation can cause the same water damage they're supposed to prevent. Proper discharge distance is critical.