For example, running wget https://www.dropbox.com
results in the following errors:
ERROR: The certificate of `www.dropbox.com\' is not trusted.
I have the similar problem and fixed it by temporarily disabling my antivirus(Kaspersky Free 18.0.0.405). This AV has HTTPS interception module that automatically self-sign all certificates it finds in HTTPS responses.
Wget from Cygwin does not know anything about AV root certificate, so when it finds that website's certificate was signed with non trust certificate it prints that error.
To fix this permanently without disabling AV you should copy the AV root certificate from Windows certificate store to /etc/pki/ca-trust/source/anchors
as .pem file(base64 encoding) and run update-ca-trust