Summary: We study the independence complexes of families of well-covered circulant graphs discovered by E. Boros et al. [Discrete Math. 318, 78–95 (2014; Zbl 1281.05073)], J. Brown and R. Hoshino [ibid. 309, No. 8, 2292–2304 (2009; Zbl 1228.05178); ibid. 311, No. 4, 244–251 (2011; Zbl 1222.05208)], and R. Moussi [A characterization of certain families of well-covered circulant graphs. Halifax: Saint Mary’s University (Master Thesis) (2012), http://library2.smu.ca/bitstream/handle/01/24725/moussi_rania_masters_2012.pdf?sequence=1&isAllowed=y]. Because these graphs are well-covered, their independence complexes are pure simplicial complexes. We determine when these pure complexes have extra combinatorial (e.g., vertex decomposable, shellable) or topological (e.g., Cohen-Macaulay, Buchsbaum) properties. We also provide a table of all well-covered circulant graphs on 16 or less vertices, and for each such graph, determine if it is vertex decomposable, shellable, Cohen-Macaulay, and/or Buchsbaum. A highlight of this search is an example of a graph whose independence complex is shellable but not vertex decomposable.