The present invention relates to the use of positively-charged unsymmetrical cyanine dyes, including novel unsymmetrical cyanine dyes, to stain cells and selectively stain intracellular organelles, with particular advantages in staining mitochondria. The dyes are generally weakly fluorescent in aqueous solution but highly fluorescent in cells and organelles, typically staining cells or mitochondria with a green fluorescence. The dyes stain mitochondria in both live and dead cells, and are retained in mitochondria even where the cells are treated with solvents that permeabilize cell and mitochondrial membranes. Mitochondria or cells stained according to this method are optionally stained with an additional detection reagent, such as a labeled antibody, labeled oligonucleotide, fluorogenic enzyme substrate, or other indicator for a specific cellular component or substructure, including another unsymmetrical cyanine stain of the same or different class.