How plants reproduce asexually and naturally?

 Vegetative Propagation

Stem , leaves , roots are vegetative parts of plants.

Flowers are reproductive parts of the plants which perform sexual reproduction. Vegetative parts are produced much before the reproductive parts in a plant.

Sometimes vegetative propagation happens in plants in addition to the sexual reproduction.

For example in banana flowers utilised for sexual reproduction where as modified stem rhizomes are used in vegetative propagation .

Some plants are vegetatively propagated with the help of roots for example sweet potato.

Some plants are propagated with the help of modified stem. For example Ginger turmeric are propagated by modified stem having buds and stored food. 

Onion and garlic are grown by modified shoot called bulb which have leaves filled with food.

Potatoes which we eat are having nodes for eyes having buds which can grow into new potato if planted in soil. These modified stems of potato are called stem tuber. They also store food . 

Suckers our modified stems in mint and chrysanthemum which are produced from base of another shoot and they grow parallel to the ground coming out of the soil to sprout new shoots . They remain themselves underground most of the part except where they produce aerial shoots .

Offsets are modified stem in aquatic plants producing bunch of leaves at their top and help water hyacinth to cover the surface of water .

Terror of Bengal is the name given to this plant ( Eichornia crassipes )