The zika virus is making the news these days.   We're hearing that for 4 out of 5 people, the virus produces no symptoms, and for the remaining unlucky 1 out of 5, the symptoms may include fever, rash, joint pain, or conjunctivitis (red eyes).   Symptoms typically begin 2 to 7 days after being bitten by an infected mosquito and may last for a week or so, just like a cold. 

We've also heard that there may be a link between the virus in pregnant women and microcephaly - the underdevelopment of the foetus' brain.   Apparently, this link is not yet proven, only suspected.

The US Center for Disease Control (CDC) has an excellent post on this matter - it does advise caution for pregnant women (e.g. avoid traveling to infected areas if you can) and women who might become pregnant while traveling to an infected area, or very soon afterwards.

The site reports that the virus only lives in our bodies for a week or two, then it is eliminated by our natural defenses, somewhat like how we deal with the common cold and flu viruses - we get them, we get sick, we get better, end of story.  This means that for women who are not pregnant, but may eventually decide to have a baby in the future, there is no risk.  The CDC website includes this Q & A:

If a woman who is not pregnant is bitten by a mosquito and infected with Zika virus, will her future pregnancies be at risk?

We do not know the risk to the baby if a woman is infected with Zika virus while she is pregnant.  However, Zika virus infection does not pose a risk of birth defects for future pregnancies.  Zika virus usually remains in the blood of an infected person for only a few days to a week.  The virus will not cause infections in a baby that is conceived after the virus is cleared from the blood.

http://www.cdc.gov/zika/pregnancy/question-answers.html

Ecuador is on the CDC advisory list, and Galapagos is in Ecuador, though I doubt if there is any conclusive evidence that the virus has made it to the islands.  There are quarantine measures in place designed to prevent alien species (such as the mosquito responsible for transmitting the virus) from reaching the islands - though I don't know at this point if this  mosquito is already there or not.  

In conclusion, unless you are pregnant, or likely to get pregnant while in Ecuador and/or Galapagos, or within a couple of weeks after your return, the CDC says there should be nothing to be worried about.