DNA is one of the most highly-charged molecules known, and interacts strongly with other charged molecules in the cell. Polycations such as histone proteins and protamines modulate DNA condensation to perform essential biological functions, and synthetic polycations are widely used to deliver genes and therapeutic oligonucleotides both in vitro and in vivo. Condensation of long double-stranded DNA is one of the classic problems of biophysics, and is reasonably well understood, but the polyelectrolyte behavior of short and/or single-stranded nucleic acids has attracted far less study despite its importance for both biological and engineered systems. We report here studies of DNA oligonucleotides (10-88 nt) complexed with various polycations, including poly(L)lysine and short polyamines. As seen previously for longer sequences, double-stranded oligonucleotides form solid precipitates, but we observed that single-stranded oligonucleotides instead undergo liquid-liquid phase separation to form coacervate droplets. Complexed oligonucleotides remain competent for hybridization, and display sequence-dependent environmental response. We observe similar behavior for RNA oligonucleotides, and methylphosphonate substitution of the DNA backbone indicates that nucleic acid charge density controls whether liquid or solid complexes are formed. Liquid-liquid phase separations of this type have been implicated in formation of membraneless organelles in vivo, and have been suggested as protocells in early life scenarios; oligonucleotides offer an excellent method to probe the physics controlling these phenomena. We also report results on polyelectrolyte core micelles formed from nucleic acids (DNA/RNA/2¯-OMe) and polylysine-PEG block copolymers, which have been proposed as smart delivery devices for therapeutic nucleic acids and peptides.