The rule of thumb is to keep ISO as low as possible to avoid the noise interference. That's because a lower ISO gives less noise and reportedly a better dynamic range/clarity in the shot. However, the technology in modern digital cameras is so sophisticated that high ISO noise is much less of a problem.

Is 1600 ISO too high?

ISO 800 is half as sensitive to light as ISO 1600. A low ISO value (e.g. 100 or 200) means low sensitivity to light. This is exactly what's needed in bright conditions in order to avoid overly-exposed photos. A high ISO value (e.g. 800, 1600 or higher) means a high sensitivity to light.

Is using a high ISO bad?

When more light is hitting the sensor of a digital camera at higher ISO, if the scene is not well illuminated there will still be noise in the shadows and darker areas of an image. The result is poor quality due to the noise in the image. The higher your ISO, the more grains in the image.