Another interpretation (SPOILERS)
OK, I agree with the memories/nostalgia thing, but I want to add another thing. It seems as if the main character is incapable of having decent realtionships. Those androids who "never responded him" are symbolic to his real relationships that end up bad and he is the reason for this. And of course, the "missed opportunity" issue which is mostly covered through the "2046 train" metaphore with the main character realising that although he'd experienced love, he would never be truly happy and there will never be the right person for him.
Just my thoughts... Great movie. I hope the other two movies are not connected, because I never knew it's a trilogy.
"We all go a little mad sometimes"
Anthony Perkins as Norman Bates - Psycho (1960)