To provide practice and assessment of computational thinking, we need specific problems students can solve. There are many such problems, but they are hard to find. Learning environments and assessments often use only specific types of problems and thus do not cover computational thinking in its whole scope. We provide an extensive catalog of well-structured computational thinking problem sets together with a systematic encoding of their features. Based on this encoding, we propose a four-level taxonomy that provides an organization of a wide variety of problems. The catalog, taxonomy, and problem features are useful for content authors, designers of learning environments, and researchers studying computational thinking.