In general, leave image stabilization on unless there’s a reason not to. It helps most when handholding at slower shutter speeds, longer focal lengths, or when your hands are unsteady.

Common times to turn it off:

• tripod use with older IS lenses that lack tripod detection, because the system may hunt for movement and soften images
• panning, if your lens doesn’t have a panning mode
• very fast shutter speeds, if you’ve actually seen image quality get worse
• video, if you want to avoid visible IS artifacts
• battery saving, especially in live view or movie mode where IS may run longer

The exact behavior is somewhat lens-specific. Newer systems often detect tripod use automatically, and some lenses have dedicated panning modes, so the old “always turn IS off on a tripod” rule is not universal anymore.

For your uses: handheld sports with a 70-200mm can benefit from IS, especially if shutter speeds dip. For long night exposures on a tripod, turning IS off is usually the safer choice unless the lens specifically handles tripod use well.