In a recent article [Minimal Cohen-Macaulay Simplicial Complexes][1] by Dao, Doolittle, and Lyle many examples of CM complexes (which happen to be minimal by there definition) are listed in Section 5. For example, included in the list are triangulations of $\mathbb{RP}^{2n}$ or the dunce hat. Some interesting examples are [A non-partitionable Cohen-Macaulay simplicial complex][2] and [A balanced non-partitionable Cohen-Macaulay complex][3] which are recent counterexamples to the "partionability conjecture."


  [1]: https://arxiv.org/abs/1905.05043
  [2]: https://arxiv.org/abs/1504.04279
  [3]: https://arxiv.org/abs/1711.05529