Binary fission is similar to mitosis. It produces two daughter cells that are genetically identical to the parent cell.
Binary fission occurs in prokaryotes. The environmental conditions can determine whether this is advantageous or not. Think about this, the daughter cells are identical to the parent. Would this advantages in a favorable environment? What about in an unfavorable environment?
A few eukaryotes reproduce asexually through mitosis. Examples are budding, fragmentation, and vegetative reproduction.
Budding forms a new organism from a small projection on the surface of the parent. Yeast reproduce through budding.
Fragmentation is the splitting of the parent into pieces that each grow into a new organism. Molds, yeasts and mushrooms can all reproduce through fragmentation.
Vegetative reproduction forms a new plant from the modification of a stem or underground structure on the parent plant. The reproduction of crocus are a great example of vegetative reproduction.