"Collections of mathematical objects":
If math is the art of finding relations between abstract objects, then a catalogue of abstract objects is a good place for a mathematician to start. So: real numbers (in order of popularity), equations, functions, formulas involving π, tilings (previously, specifically nonperiodic), rings and their properties, finite group representations, packings of equal circles in a square, triangle centers (previously), top ten lists of prime numbers, integer sequences (previously, extremely previously), combinatorial statistics, graphs, movies, fundamental theorems, counterexamples.
