Pólya-Szegő seems unsurpassed as a graduate level problem book on classical function theory. Other classic examples are:
P. Halmos, A Hilbert space problem book, and
A. Kirillov and A. Gvishiani, Theorems and problems in functional analysis, available in English and French, bseides the Russian original, and
I. Glazman and Yu. Lyubich, Linear analysis in finite-dimensional spaces, translated from the Russian.