Interfaces between spindle microtubules and kinetochores were examined in diverse species by electron tomography and image analysis. Overall structures were conserved in a mammal, an alga, a nematode, and two kinds of yeasts; all lacked dense outer plates, and most kinetochore microtubule ends flared into curved protofilaments that were connected to chromatin by slender fibrils. Analyses of curvature on >8,500 protofilaments showed that all classes of spindle microtubules displayed some flaring protofilaments, including those growing in the anaphase interzone. Curved protofilaments on anaphase kinetochore microtubules were no more flared than their metaphase counterparts, but they were longer. Flaring protofilaments in budding yeasts were linked by fibrils to densities that resembled nucleosomes; these are probably the yeast kinetochores. Analogous densities in fission yeast were larger and less well-defined, but both yeasts showed ring- or partial ring-shaped structures girding their kinetochore microtubules. Flaring protofilaments linked to chromatin are well placed to exert force on chromosomes, assuring stable attachment and reliable anaphase segregation.