1. Gutters for roof is also used to drain water when raining. Without gutters, during heavy rain, rain will drain from roof directly, which mean a small water fall....
2. Water has to be drained away from the house for about 3ft (if I remember correctly - correct me if I am wrong about the actual distance), this is according to building codes. If it's not done (for the sake of argument, we will skip weather it will harm your foundation or not), you will have difficulty to claim insurance during water damage to foundation
3. Your house's elevation should be above grid, which means when water drained from gutters will follow grid and go down instead of backing to your foundation. .