The simplest organism that can learn?
I don't know if it is definitively the simplest, but the simplest organism with a nervous system that has been studied extensively is probably C. elegans, which is definitely able to learn.

Some basic learning abilities have also been shown in amoebae.



References:


Ardiel, E. L., &amp; Rankin, C. H. (2010). An elegant mind: learning and
memory in Caenorhabditis elegans. Learning &amp; Memory, 17(4), 191-201.
Saigusa, T., Tero, A., Nakagaki, T., &amp; Kuramoto, Y. (2008). Amoebae
anticipate periodic events. Physical review letters, 100(1), 018101.