Ooohh... this one is interesting.
As for my favourite Anime episodes, there are a few sticking out. Most of them from the Indigo Saga.
Episode 1, of course, is flat out awesome. It starts with a professional Pokémon battle between mystic top trainers. It shows how Pokémon live in a society alongside humans. The Dodrio coo-cooing to wake up Pallet Town. All the merchandise in Ash's room.
The rest of the Indigo Saga is also fantastic. Let's just say all of it in general, with a special mention of the great race. I love the guy riding on an Electrode, probably chosen because it was the fastest Pokémon at the time (as in, the highest speed stat. I believe the Pokémon with the greatest landspeed is Arcanine - a Pokédex entry gives it an alleged cruise speed of 417 km/h). However, it turned out to be wildly impractical to ride. The Gym battles were also great, especially Cinnabar Gym with Charizard vs. Magmar.
However, I guess my favourite episode/arc is at the start of the Indigo League, when you finally see how the League isn't built specifically for Ash, and that his journey had a purpose all along. There is a parade. Big lobbies where trainers have to register, and where tournament matchups are drawn (using Magikarp and a fishing rod, if memory serves me correctly). A buffet restaurant nearby gives a free plate to all participating trainers. There is an Olympic village, a big torch to be lit, thousands of spectators (now, where are all those in the games?), speakers, themed battlefields, Prof. Oak comes to visit...
You see the big logistics organization required to run the big tournament, Ash is finally "one of the crowd", and he doesn't even win it all - but he performs very well. The matches also have a very official feel to them, as to underline that things have gotten professional. There are big stadiums with clear lines drawn in the fields, there are platforms trainers are required to stand on, a referee with flags declare wins or losses, and the match status is shown on a big screen.
It's the ultimate culmination of the Pokémon saga, the arc it would have ended with if they hadn't decided to continue the series. It would be a worthy end, definitely. I'll remember those episodes fondly.
Another mention should be made about a later episode, though: In the Hoenn saga, where Groudon meets Kyogre. This is the episode acknowledging the power of Legendary Pokémon, and man do they show that these titans are unstoppable when on the loose. It's like they wanted team Aqua/Magma to capture them, so they could be brought together for a fight. Kyogre takes things calmly, and escapes the Magma ship easily. Groudon takes control of Pikachu to steer events so that it can be set free. It has to be one of my favourite moments from Pokémon, when Groudon's eyes snap open, as if it's saying "enough of this, I wanna fight!", and it tears apart the chains tying it down in its container. You then cut to an exterior shot, where a massive explosion follows. A huge plume of fire and smoke rises to the sky. Then Groudon's silhouette emerges from its center, calmly walking away from the burning remains of Team Aqua's container.
Then follows an epic battle. Kyogre sending tsunamis the size of mountains towards the island, and Groudon obliterating them with Solarbeam. Multiple vicious tornadoes appear, only to be evaporated in the harsh sunlight. Not to mention the earthquakes. The two ancient Pokémon eventually calm down, Groudon walking into a volcano and Kyogre diving into an underwater trench, to sleep again for thousands of years until they meet again one day.
As for my favourite movie, it strangely involves the final member of the Weather Trio. Movie 7, Destiny Deoxys, is a favourite of mine because:
1) It has no true villain
2) The world isn't at stake
3) Ash isn't "the chosen one", though of course he has to play hero in the end.
This movie is mostly about Rayquaza and its relation to Deoxys. Rayquaza is the king of the sky, flying wherever it damn pleases around the ozone layer. Everybody fears and reveres Rayquaza, it is top dog and knows it.
However, its pride is badly hurt when a Deoxys has the audacity to almost crash into it where it flies. It's not only an intrusion of its personal space, it's flat out challenging Rayquaza's authority. Furious, Rayquaza sets out to destroy the insolent Deoxys. Its Hyper Beams rip the land apart, it destroys a research station with Outrage, thousands of wild Pokémon flee in panic as the battlers duke it out. Finally, after being tossed into the sea by Deoxys, Rayquaza manages to defeat it, firing a Hyper Beam into its most vulnerable spot at point-blank range. Deoxys is obliterated, and Rayquaza is the king of the sky once again. Peace is restored.
However, Pokémon attacks can't kill, the defeated will rise again sooner or later. This is usually a matter of seconds or minutes, but with the power of Rayquaza's Hyper Beam, it takes four years. Deoxys makes the error of calling out to its fallen comrade, who apparently collided with a comet at high enough speeds to fuse them together. Rayquaza hears/sees the call, and realizes its mortal enemy has returned. It sets off to LaRousse city, to extract its revenge. The residents of LaRousse clearly know how much power Rayquaza holds, as they promptly evacuate the city when they see it is coming. An epic battle follows.
However, as they fight, Rayquaza realizes there were reasons why Deoxys didn't pay attention that time back in the Antarctic. Slowly, it dawns that Rayquaza itself may be the aggressor, and Deoxys was hunted down and sent into a coma because of a misunderstanding. They finally wrap it up, and Rayquaza leaves, realizing he still is the uncontested king of the skies. Deoxys didn't want to overthrow Rayquaza, it was simply trying to protect its friend.
There is also some boring stuff about Ash, but he does little to influence the overall plot and turn of events. True, he saves the day when the cube robots go haywire, but that almost felt tacked on. Apart from that, though, Ash and co. are simply caught in the crossfire between two legendary Pokémon, and their goal is first and foremost to survive and get away from the city, instead of saving the world as usual. Nobody have any villainous intent here (apart from Team Rocket, who really shouldn't count), a fresh contrast to most of the other movies. It's simply a disaster/monster movie, where the city-crushing monsters express character development. That's kind of original.