For my historical flight tracking on my.flightar24 & flightmemory, which I've tracked down back to 2001 - I've looked up just about every tail number I've flown on!
There's a few tail number that just seem to be lost to any records - I've tried both free & paid services. I found flightstats to have generally the best paid archives just FYI
But if you're looking for
domestic US flight info on aircraft type, tail #, or flight timing, Bureau of Transportation Statistics (BTS) keeps good historical records:
https://www.transtats.bts.gov/ONTIME/
The search interface is a little clunky, but some guy made simplified interface that searches the same DB which you can find here:
Aircraft Tail Number Lookup