The spatial scan method is extremely popular for identifying disease clusters using disease count data. The original spatial scan method is relatively simple, very fast, and has high power for detecting circular clusters. Free, publicly-available software led to its widespread use in a variety of contexts. However, the original spatial scan method can struggle to identify non-circular clusters. Many extensions of the original method have been proposed to better detect irregularly-shaped clusters compared to the circular scan method. We briefly describe many of the popular spatial scan method extensions (e.g., Upper Level Set, Flexibly-shaped, Dynamic Minimum Spanning Tree, Fast Scan, etc.). We then compare the performance of the various methods using power, specificity, and sensitivity by applying these methods to 61 publicly-available benchmark data sets that utilize 41 different cluster shapes. The comparisons go into more depth and have more competing methods than previous studies of this topic, allowing us to draw broader conclusions about the best performing methods.