The reaction of 2,6‐pyridinediylbis(3‐pyridinyl)methanone (abbreviated as L) with various silver(I) salts yielded a series of complexes, namely, [Ag2(L)2](ClO4)2 (1), {[Ag2(L)2](ClO4)2}∞ (2), {[Ag2(L)2](NO3)2}∞ (3), {[Ag2(L)2](C2F5CO2)2}∞ (4), {[Ag2(L)2](C3F7CO2)2}∞ (5), and {[Ag2(L)2](O2CC3F6CO2)·2H2O}∞ (6), which exhibit a common dinuclear metallacyclic [Ag2(L)2]2+ skeleton that involves linear‐dicoordinate AgI and μ2‐N,N‐bridging L. Complex 2 is a polymorph of 1 obtained by the solvent‐medium tuning effect, and it has an {[Ag2(L)2]2+}∞ infinite‐chain structure. In complexes 3–6, the argentophilic interaction plays an important role in connecting the [Ag2(L)2]2+ units to form a similar {[Ag2(L)2]2+}∞ chain structure to that in 2, although the counteranions are markedly different. The copper(II) complex {[Cu2(CH3CO2)4(L)]·2H2O}∞ (7) exhibits a zigzag‐chain structure composed of an alternating arrangement of L and the Cu2(CH3CO2)4 paddlewheel cluster. In the supramolecular architectures of 1–7, the counteranions engage in multiple noncovalent interactions, and the presence of unusual types such as O/F(anion)···π, O/F(anion)···C=O, and C=O···π are noted and discussed.