Medical image analysis plays an important role in clinical diagnosis. In this paper, we examine the recent Segment Anything Model (SAM) on medical images, and report both quantitative and qualitative zero-shot segmentation results on nine medical image segmentation benchmarks, covering various imaging modalities, such as optical coherence tomography (OCT), magnetic resonance imaging (MRI), and computed tomography (CT), as well as different applications including dermatology, ophthalmology, and radiology. Those benchmarks are representative and commonly used in model development. Our experimental results indicate that while SAM presents remarkable segmentation performance on images from the general domain, its zero-shot segmentation ability remains restricted for out-of-distribution images, e.g., medical images. In addition, SAM exhibits inconsistent zero-shot segmentation performance across different unseen medical domains. For certain structured targets, e.g., blood vessels, the zero-shot segmentation of SAM completely failed. In contrast, a simple fine-tuning of it with a small amount of data could lead to remarkable improvement of the segmentation quality, showing the great potential and feasibility of using fine-tuned SAM to achieve accurate medical image segmentation for a precision diagnostics. Our study indicates the versatility of generalist vision foundation models on medical imaging, and their great potential to achieve desired performance through fine-turning and eventually address the challenges associated with accessing large and diverse medical datasets in support of clinical diagnostics.