Where can I find historical data on arrival and departure times of a particular flight?
The nearest to official source would be the FAA data available at https://transtats.bts.gov/ONTIME/. However, this data is always several months behind (eg, they currently have up to June 2019 as of August 2019), and not as easy to search for specific flights as either of the above two sites.
For both Flight Stats and FlightAware, you'll need to create an account and buy a subscription, unless the data you want is only a few days old.
Please be aware of the fact, that for instance flightrights does not allow to use their data for any passenger claims, see https://developer.flightstats.com/about/terms_for_paid_accounts
The URL has changed to https://www.transtats.bts.gov/Fields.asp?Table_ID=236
@domen some airlines provide on-time, cancellation data for specific routes in their apps. Other than governmental aviation regulatory bodies, you would probably have to inquire of the airlines directly.
The airlines are a bit hesitant to do that. They will often have a conflict of interest, since passengers want that data for compensation claims.