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.