Best... any where I've been going to some fantastic places and/or people, to places I've actually wanted to go. I can't pick just one.
Worst... one where I was denied boarding (ask me around a beer some day in the real life, not going to elaborate more online about that). Also the last Ryanair flight I had bought (free flights from Cork to Dublin, the "free" translated to 70 euros in fees. And that is on the list because I still had to leave the return unused as I would have had 1.6 kg over 15 kg of their checked in limits, so it was cheaper to do the 4+ hours in bus than pay the overweight fee - I already had that ticket). Plus a few flights get close to being added to that list, when I've had my seat too close to loud children or screaming babies (and once close to a girl who was terrified of flying, so she was screaming the whole flight. Fortunately that was less than 3 hours).
My best was to my first Army posting to Japan. The United 747 was mostly empty that flight and the flight crew let me sleep across the empty center seats during the 18 hour flight. I almost 6 slept hours straight during that long flight. The the ANA Japan domestic flight was cool because all Japan flights their was a camera on the front nose gears and would turn on during take offs and landings.
The worst was coming back on a chartered plane from the Air Force from Kadena to LAX. Halfway over the Pacific we went through one of of those no air pockets and dropped a couple thousand feet instantly. Since it was an Air force MAC flight there were a lot of small screaming kids on the flight too.
Any best flight is totally overshadowed by the worst.
Worst one goes back a while. I was flying out of Miami to Paramaribo. It was Terminal C IIRC. Sitting in the waiting room, I saw a technician standing on a step ladder with his head and shoulders in the wing. Then the guy came out, reached down and pulled a length of baling wire off a spool and went back into the wing. After two more trips to the bailing wire he went for a roll of duct tape. I was so-oo happy when they canceled the flight and put us up in a hotel.
Next day we had to take a detour, we went to Mexico City to pick up spectators the World Cup '86. We landed, took on passengers and then had to disembark. We stayed three days in Mexico City before the plane was finally cleared to take off. The ride to Paramaribo was a nail biter, lots of turbulence and anxiety about the whatever the repairs were. I was so happy to get home, even 4 days late.
According to friends on the crew, the guy who sat on the clearance after the repairs told the Suriname Airways guy "the yellow form and the blue form are all here, but where is the green form?" Gotta love third world bureaucrats.
I was on an Egyptair flight once that had a camera on board looking down so you could see the ground. It had an inflight screen alternated between the panorama shot and a statistics page. When we were coming into JFK over water you could see the boats chugging along and see their wakes. There was a large black tubular figure that seemed to be under the water ( no wake ). It looked kind of like a hand rolled cigarette.
The screen would flip to the stats page and come back and the shape would still be there. I wondered for a long time about what it could possibly be. I thought a whale or a sub or something just below the surface of the beautiful waters. But I realized that even with parallax view it would have to be moving very fast, I felt like an idiot when it finally hit me that it was the shadow of the plane. Durrh! :-/