Electrospinning is a new technology whose scope is gradually being developed. For this reason, the number of known polymer–solvent combinations for electrospinning is still very low despite the enormous variety of substances that are potentially available. In particular, electrospinning from low-toxic solvents, such as the use of dimethyl sulfoxide (DMSO) in medical technology, is rare in the relevant scientific literature. Therefore, we present in this work a series of new polymers that are applicable for electrospinning from DMSO. From a wide range of synthetic polymers tested, poly(vinyl alcohol) (PVOH), poly(2ethyl2oxazolene) (PEOZ), and poly(vinylpyrrolidone) (PVP) as water-soluble polymers and poly(styrene-co-acrylonitrile) (SAN), poly(vinyl alcohol-co-ethylene) (EVOH), and acrylonitrile butadiene styrene (ABS) as water-insoluble polymers were found to be suitable for the production of nanofibers. Furthermore, the influence of acetone as a volatile solvent additive in DMSO on the fiber morphology of these polymers was investigated. Analyses of the fiber morphology by helium ion microscopy (HIM) showed significantly different fiber diameters for different polymers and a reduction in beads and branches with increasing acetone content.