DNA nanotechnology takes advantage of the predictability of DNA interactions to build complex DNA-based functional nanoscale structures. However, when DNA functional and responsive units that are based on non-canonical DNA interactions are employed it becomes quite challenging to predict, understand and control their thermodynamics. In response to this limitation, here we demonstrate the use of isothermal urea titration experiments to estimate the free energy involved in a set of DNA-based systems ranging from unimolecular DNA-based nanoswitches to more complex DNA folds (e.g. aptamers) and nanodevices. We propose here a set of fitting equations that allow to analyze the urea titration curves of these DNA responsive units based on Watson-Crick and non-canonical interactions (stem-loop, G-quadruplex, triplex structures) and to correctly estimate their relative folding and binding free energy values under different experimental conditions. The results described herein will pave the way toward the use of urea titration experiments in the field of DNA nanotechnology to achieve easier and more reliable thermodynamic characterization of DNA-based functional responsive units. More generally, our results will be of general utility to characterize other complex supramolecular systems based on different biopolymers.