We present a systematic density functional theory study of the electronic structure of copper phthalocyanine (CuPc) using several different (semi)local and hybrid functionals and compare the results to experimental photoemission data. We show that semilocal functionals fail qualitatively for CuPc primarily because of underbinding of localized orbitals due to self-interaction errors. We discuss an appropriate choice of functional for studies of CuPc/metal interfaces and suggest the Heyd-Scuseria-Ernzerhof screened hybrid functional as a suitable compromise functional.