How do I find the registration or serial number for the aircraft I flew on specific trips in the past? I understand that there are various paid subscription services that allow me to search back up to a year in the past for the IDs of any flight and the histories of any aircraft.

Is there a free (or one-time fee) service or API for identifying the aircraft I've flown on specific dates and flights in the (up to several years) past?
The US (if that's your area of flying) is very kind in publicly releasing stats compared to other territories, but the answer is still you can't without a paid service.

See:


Where can I get information on ATC facility activity, like the number of flights handled in a month?
How can I get historic flight data by N-number?


In short: The FAA only keeps broad records that do not contain information such as tail numbers.

Start a personal flight journal for future flights, it's a hobby some enjoy. I did at one time, and when I couldn't catch the registration, I asked the flight crew.