The first three compounds based on a {copper–thiocyanate–dabco} combination, namely, (Hdabco)[Cu2(NCS)3] (1), (H2dabco)[Cu(NCS)3] (2), and [Cu(Hdabco)2(NCS)4]∙2dmso (3), where dabco = 1,4-diazabicyclo[2.2.2]octane were synthesized and characterized by single-crystal XRD, elemental analysis, Raman, and partial IR spectroscopy. In copper(I) derivatives, the influence of the charge of the organic cation on the dimensionality of the crystal structure is observed. Thus, in the case of1, monoprotonated Hdabco+cations provide the template for the formation of a polymeric anionic 3D framework {[Cu2(NCS)3]−}n, while in the case of2, diprotonated H2dabco2+cations together with discrete [Cu(SCN)3]2−anions generate a simple ionic 0D structure with an island-like crystal lattice. The anionic {[Cu2(SCN)3]−}nframework has infinite square channels of 10 × 10 Å size running along the 001 crystallographic direction. In3, both the Hdabco+and thiocyanato units behave as terminal monodentate ligands attached to copper(II) centers via N-donor atoms, forming neutral molecular complexes with an elongated (4+2) octahedral environment. The crystallization molecules of dmso are hydrogen bonded to the protonated parts of the coordinated dabco molecules. A series of by-products Cu(SCN)2(dmso)2(4), (Hdabco)SCN (5), (H2dabco)(SCN)2(6), and (H2dabco)(SCN)2∙H2O (7) were identified and characterized.