DNA has played an early and powerful role in the development of bottom-up nanotechnologies, not least because of DNA's precise, predictable, and controllable properties of assembly on the nanometer scale. Watson-Crick complementarity has been used to build complex 2D and 3D architectures and design a number of nanometer-scale systems for molecular computing, transport, motors, and biosensing applications. Most of such devices are built with classical B-DNA helices and involve classical A-T/U and G-C base pairs. However, in addition to the above components underlying the iconic double helix, a number of alternative pairing schemes of nucleobases are known. This review focuses on two of these noncanonical classes of DNA helices: G-quadruplexes and the i-motif. The unique properties of these two classes of DNA helix have been utilized toward some remarkable constructions and applications: G-wires; nanostructures such as DNA origami; reconfigurable structures and nanodevices; the formation and utilization of hemin-utilizing DNAzymes, capable of generating varied outputs from biosensing nanostructures; composite nanostructures made up of DNA as well as inorganic materials; and the construction of nanocarriers that show promise for the therapeutics of diseases.