I dig Firefly and Cowboy Bebop. Also the first two MST3K openings but I'm less on board with everything that came after.
I'll add two openings I like because they are effectively theses for their shows:
First Rome. Not a single lead actor is pictured and the camera never focuses on anyone's face. It's all about the city, the graffiti, the muck that comes about when real people make an impact on their world, and that impact isn't always the clean white marble we're used to thinking of when we think of Roman relics. It also creates an excellent bridge into the cultural mindset of classical Romans- sure, their attitudes toward sex and violence were different than ours today, but they're not so different that we can't comprehend them.
Next: Paranoia Agent. This series is a beautifully scathing criticism of many facets of Japanese society, yet both inside and outside Japan it seems to get very little recognition as anything other than "weird". The music to me is like a soundtrack to Tokyo life, but it's the images that I like best and I find it odd that people often react to this OP like it's some inscrutable puzzle. We start with the main character Tsukiko depicted in an archetypal Japanese suicide attempt (It might at first seem that she's just standing on a tall building, but if you look carefully you see she's holding her shoes. Apparently many Japanese people who kill themselves by jumping off of buildings take off their shoes first.) laughing mindlessly. The OP then procedes to show us all the other principle characters of the show in terrible predicaments (submerged after a tidal wave, falling from the sky, in garbage dumps, etc) laughing in the same mindless way, eventually leading to the old man laughing on the Moon as the Earth is wracked by nuclear explosions. I don't want to give away the plot, but this denial of one's circumstances to force an outward appearance of happiness essentially ties into the thesis of the show.
The tidal wave scenes especially carry weight for me in the aftermath of the Tohoku Earthquake and Tsunami. It's a precognizant echo of the odd way that in the weeks following people were constantly inundated with horrible news about destruction, devastation, and ruined or lost human lives, yet people who were not directly affected seemed to feel that they must go about their normal daily routines as though they felt nothing.