There are several pros and cons for sexual and asexual reproduction.
Pros: Only one parent is needed to reproduce; it tends to take a shorter amount of time; the offpsring have identical characteristics to their parent; in general, asexual reproduction is more reliable.
Cons: There is almost no chance of evolution taking place to any appreciable degree; bad or damaging genetic traits (if they exist in the parent)
Pros: Genetic mixing allows for greater variation in the offspring; the chance of evolution taking place is increased because of the variability of the offspring; the offspring have a mixture of traits so damaging genetic traits might not be passed on
Cons: Two parents are needed to reproduce; finding a mate; even after fertilization has occured there is a chance that the offspring will not make it to full gestation; sexual reproduction also takes much longer
Example of an animal that reproduces sexually and asexually: Jellyfish can reproduce by budding (asexually), but they primarily reproduce sexually.
One of the most important things a species must have to insure its dominance is the ability to reproduce. Some organisms reproduce sexually, requiring two parents, while others reproduce asexually, requiring only one parent. Sexual reproduction provides greater genetic variation, as it combines the DNA from two parents, producing offspring that are not genetically identical to either parent. Asexual reproduction requires only one parent and produces offspring that are genetically identical to the parent. Most mammals reproduce sexually. Sea stars and the hydra are two organisms that reproduce asesually. Then, there are organisms like yeast and some bacteria that reproduce using both methods. It would seem to me the environment the organism is living in might have some influence on the particular method of reproduction an organism might evolve into.