Mr. Jack-
Yes, there are many species that can reproduce sexually and asexually. Not to nit-pick but aphids are not one of them. Aphids like a number of sexually reproducing species use parthenogenesis. While parthenogenesis doesn't use sex and therefore seems like it is asexual, it is actually still sexual reproduction. In true asexual reproduction a haploid or diploid cell (depends on taxa) or group of cells can organize into a complete replica of the adult called a clone. In parthenogenesis a haploid egg of a diploid species either fuses with another egg from the same parent (just like it would in standard sexual reproduction) or undergoes mitosis becoming diploid then behaves like a fertilized egg. The key difference is that in asexual reproduction the daughter product is a clone of the adult. In parthenogenesis, even though a single parent is responsible, the normal shuffling (recombination) occurs so that embryo is similar but not a clone. In most animal species parthenogenesis is an accident, but several taxa (including insects like aphids) have it as a major reproductive tactic. Some groups of rotifers (bdellids) use parthenogenesis alone.
To further complicate things parthenogenesis is different from from selfing, sexual reproduction in a simultaneous hermaphrodite. In those species their sperm fertilize their eggs. The fact that most simultaneous hermaphrodites have distinct barriers to selfing suggests that this is not optimal. For example, some terrestrial gastropods (snails and slugs) will only self when in isolation for an extended period.
I look forward to this topic developing. I am going to be offline for the next 4 days but look foreward to seeing this thread develop. My MS work was on the evolution of sexual systems in crustaceans so hope I can contribute.
Doctor Bashir: "Of all the stories you told me, which were true and which weren't?"
Elim Garak: "My dear Doctor, they're all true"
Doctor Bashir: "Even the lies?"
Elim Garak: "Especially the lies"