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.