I'd read somewhere that red-blood cells don't have any of the typical cellular machinery in them; no nucleus for example.
Turns out this is true only for mammals. This Twitter thread goes over some of the theories as to why mammals don't have nucleated red-blood cells.
It could be because the mammalian genetic code is quite large, and not having it in the RBCs helps the cells be smaller and more mobile. Or because cells without nuclei can't become cancerous, so large mammals can live longer if a significant proportion of their cells don't have nuclei.