Is it possible to use the API to do something like send an email on a particular date that is in a custom field (e.g. birthday)? So each day the API would be ran and an email would be sent to people with that date in a custom field?
What you're describing here is how our autoresponders work, but at the moment they cannot be setup or triggered via the API, sorry.
I've added a vote for this request on your behalf, and we'll be sure to update this thread should we release this functionality.