Binary fission is the process of parent cell splitting into two equal daughter cells. It takes place in prokaryotes (bacteria and archaea) only.
Budding is the process similar to binary fission the daughter cells grow from the parent's body and are detached to form separate individuals in time. The offsprings are always smaller than the parents. This method is observed in yeast along with lower multicellular life forms like hydra.
Spore formation or sporogenesis takes place in many multicellular organisms via mitosis and meiosis cell cycles. Spores formed develop into haploid (meiosis) or diploid (mitosis) individuals after dispersion. This method is even found in conidium fungi (not yeast).
Vegetative propagation involves forming of full offspring by a part of the parent plant, found mostly in higher plants.
Parthenogenesis is the process of developing unfertilized eggs into individuals without fertilization, this is brought about by hormonal therapy and is a common occurrence in horticulture (seedless fruits).