I wasn't born yet when the Mewtwo movie came out, so my experience is a bit different from the comments here. I watched it much later, so it didn't have the same impact on me. I believe Donphan was teased during that movie before Johto came out? That must have been crazy.
I don't remember the first one I watched because I was probably too little to keep track, but I feel like it could have been the Entei one at some point on TV (years after the original release). The ones I remember more clearly are from around generations 3 and 4. I could say that the Lucario and Mew one is where I started to get more invested in the movies. I also have clear memories of crying with the Manaphy movie; that was probably the first time a Pokémon movie hit me that hard as a kid. But overall, the Darkrai movie is my all-time favourite. I remember watching it on TV a few times.
The Jirachi and Deoxys movies were never released here, so I completely missed them until many years later when I watched them in English. It was a shame, because I would have absolutely loved them as well as a kid.
I really liked when they mixed two generations in the same movie. For example, the Pokémon that appear in the Latios/Latias one are mostly from Johto, but the main legendaries were from Hoenn. I can say the same about the Lucario and Manaphy movies. I guess it was a kind of exciting feeling to know that they were soon going to the new generations.
PS: does anyone else miss when movies took place in cities heavily based on real-life locations? As a half-Spanish and half-Italian person, Alamos Town and Alto Mare are probably my favourite places in the Pokémon world.