The Pokemon opening (original, that is) was so widespread that nearly anyone of my age would remember it with fond memories. Other anime like Digimon and Yu-Gi-Oh also aired at around the same time, but I can't remember anything about them; but, to this day, there are memes on Facebook about 'catching them all' and 'Ash turning around his hat' that would unite people of all persuasions. Indeed, if I mention the phrase "I want to be the very best", then that gets the nostalgia going in me.
On a more personal note, I love love love the music from Cowboy Bebop. Love! It! All jazz-funky and cool and whatnot.