I count myself as very lucky to have been aboard a sales demo flight in Concorde from Abu Dhabi to a point halfway to India and return, supersonic most of the way, and on the return flying about 300m from and level with the outbound condensation trail. Guests were invited up to the flight deck for a few minutes each and saw what M2 really looks like. I still have my certificate, signed by Brian Trubshaw, that all guests were given. It records a max speed of M2.05, max altitude 57,500 ft, supersonic 46 minutes, total 1 hour 16 minutes, 29th August 1974.
A little over a decade later, I was doubly lucky to blag a jump-seat ride in Concorde all the way on a flight from/to Exeter, north to Bristol Channel, west to the transatlantic acceleration point, round the Scilly Isles, back along the English Channel, slow down and land. The FO was flying the whole trip (for currency, that's why BA did all those regional visits) and as we came down the glideslope I could see that we were going to touch down halfway along the runway, go off the far end down into the village at Clyst Honiton, and die in a huge fireball. I was rigid with terror, but managed not to whimper out loud. Then, while we were still very high the main wheels touched down precisely on the markers, followed by the nosewheel. Another memorable moment was joining the westbound track to the acceleration point behind the scheduled Concorde service to the USA. As it reached the point the Captain said "watch this" just as the nose went up, 4 sheets of flame erupted from the engines, and the aircraft climbed away like a rocket. "I've never seen that", said the Captain, "Amazing".