Plasma medicine is a new field focusing on biomedical and clinical applications of cold gas plasmas, including their anticancer effects. Cold plasmas can be applied directly or indirectly as plasma-activated liquids (PAL). The effects of plasma-activated cell growth medium (PAM) and plasma-activated phosphate buffered saline (PAPBS) were tested, using a plasma pen generating streamer corona discharge in ambient air, on different cancer cell lines (melanoma A375, glioblastoma LN229 and pancreatic cancer MiaPaCa-2) and normal cells (human dermal fibroblasts HDFa). The viability reduction and apoptosis induction were detected in all cancer cells after incubation in PAL. In melanoma cells we focused on detailed insights to the apoptotic pathways. The anticancer effects depend on the plasma treatment time or PAL concentration. The first 30 min of incubation in PAL were enough to start processes leading to cell death. In fibroblasts, no apoptosis induction was observed, and only PAPBS, activated for a longer time, slightly decreased their viability. Effects of PAM and PAPBS on cancer cells showed selectivity compared to normal fibroblasts, depending on correctly chosen activation time and PAL concentration, which is very promising for potential clinical applications. This selectivity effect of PAL is conceivably induced by plasma-generated hydrogen peroxide.