Solty Rei

Solty Rei is a Manga and 26-episode Anime series that follows Roy Revant, a widowed bounty hunter who captures criminals for the Maverick Hunters agency (not that one), in a city where a phenomenon called the Aurora Shell prevents air travel (anything approaching is struck by lightning) and interferes with electronics. Then, Roy's rather unhappy life is inverted when an unusual girl named Solty literally falls into his life...

Tropes:

Affably Evil: Ashley Lynx
After the Credits: Watch through to the credits of "The Future" (the finale episode) to get an epilogue showing the true ending.
After the End - The "Blast Fall", an event that didn't quite destroy civilization, but nonetheless totally changed society.
AI Is a Crapshoot
Alliterative Name - Roy Revant, Rita aka Rose Revant, Miranda Maverick.
Amazon Brigade - The RUC girls, anyone?
Anachronic Order - In one specific case: If you're watching the DVD set, after episode 9, go to the last disc and watch "B1" & "B2", then go back to 10. B1 & B2 were interquels, set between 9 & 10, but cut from the Japanese broadcast. It's pretty funny, too.
Anti-Hero - Roy's initial character. He changes as the series goes on.
Badass Adorable - Solty.
- With a side of Cute Bruiser.
Beach Episode - Well, a pool episode - Waterside Panic. Fulfills the trope function of putting the cast in swimsuits.
Beware the Nice Ones - And don't try to electrocute them either. "I hate bad people!"
Big Bad: R.U.C. Director Ashley Lynx (at least until the final episode)
- AIs behind the man: Eunomia and Eirene, Dike's (Solty's) "sisters"
Brainwashed - It is never really clear if Rose was or was not, as the series even mentions that would be a bad idea because it could hamper her performance. It can be assumed that it may have been used earlier on her to prevent her from contacting anyone.
Bratty Half-Pint - Kasha, who regularly bosses her mother around.
Conspicuous CG - It's Gonzo.
Dead Little Sister - Roy's daughter, Rita Revant, who is missing; Roy believes her to be alive. During the series, Rose is revealed as Rita, her DNA and memories affected by the Blast Fall.
Distant Finale: Takes place several years after the climax, covering how all the protagonists are doing, with the exception of Solty, who had sacrificed her life saving the world from a meteor. After the credits, however, it skips forward again 12 years after that, where Roy, in space, discovers the frozen body of a rotted, but still conscious, Solty floating with the rest of the space debris, and breaks down in tears.
Diving Save - Done multiple times, by both Roy and Solty.
Drives Like Crazy - Integra.
Easy Amnesia - After hitting a metal beam headfirst, Solty can't remember her past or her real name.
Expy - Roy is arguably an older and even more bitter version of Rick Deckard, with his hairstyle, trenchcoat and perma-stubble fitting said ex-cop to a tee; although his relationship to androids is much more cordial.
Faking the Dead - Rose.
Fan Service - The RUC Transformation Sequence, Solty's frequent backside shots, and the fact that there is a shower or bath scene nearly every episode
Fond Memories That Could Have Been - Roy Revant, Solty's aloof and coldly distant adoptive father frantically pleaded for his little girl to not go through with the suicidal Heroic Sacrifice to save the planet, even going as far as telling her that he would take her to the amusement park like any father would his daughter. She simply smiles with tears in her eyes, and says that she's happy to have been his daughter, and bravely steps into the shuttle to her doom.
Get a Hold of Yourself, Man! - Miranda doesn't just hit Roy to bring him out of his Heroic BSOD, she beats the tar out of him. It's stated that this isn't the first time concussive maintenance was applied.
Goggles Do Nothing - Kasha wears pink goggles on her head for no readily apparent reason.
Gratuitous English - "I lost my husband and he lost his doughter."
Hair Colors - Solty, with her grass-green hair and eyes.
Healing Hands - Solty. It's not as perfect as the trope usually is, but it's better than the alternative.
Heroic BSOD - Roy after Rose's "death".
Heroic RROD - Integra is limited to three accelerations, or she risks life-threatening neurological damage.
Hidden Eyes - Solty, just before going Badass.
Hollywood Cyborg - "Resembles".
Hot Shounen Mom - Miranda Maverick, though she's adoptive.
Huge Guy, Tiny Girl - Roy and Solty.
Humongous Mecha - Walking tank variant.
If You Kill Him You Will Be Just Like Him - Everybody present pulls this on Rose to keep her from killing the man who murdered her best friend when she was just a child. It works but as soon as Rose is out of sight and earshot, her brother Larry kills the murderer anyway.
I Know You Are in There Somewhere Fight - Solty, to Rose. It works.
Ill Boy - Will, the unfortunate victim of medical malpractice.
In the Name of the Moon - Rose Anderson likes to do this.
I Owe You My Life - The reason Solty starts following Roy around.
Intergenerational Friendship - Kasha and Silvia, following their stalking tour together.
It's Personal - Rose in the episode Revenge.
Jerk with a Heart of Gold - Roy.
Just Like Robin Hood - Rose and her brothers become thieves to help provide medicine and other supplies for the 'unregistered' residents.
Laughing Mad - Accela, during her temporary Freak-Out.
Lethal Chef - Will. When you'd rather eat ~~MREs~~ "ration packs" than someone's cooking...
- Solty starts off that way, but improves dramatically with practice.
Let's Get Dangerous - The weird little girl looks harmless, right up until she punches you into the next postal code.
Line-of-Sight Name - Solty, from an album cover.
Long-Lost Relative
Love Makes You Crazy - Ashley Lynx, who is the main antagonist until the final episode.
Made of Explodium - A scanning machine blows up from just trying to examine Solty.
Manly Tears: Roy sheds some genuinely believable manly tears when it's known that he might lose one of his daughters, Solty, because of the events of the final episode (staying after the credits shows that Solty survived).
Master Computer - Eunomia
Meaningful Echo - Will, who Solty befriends in the desert, often states something and then says, "just kidding!" due to his carefree nature. This happens constantly during his episode until the last time, when he tries to hide the fact that he loves her, even when he knows he'll die soon. After he dies, Solty begins to use that saying from then on, to remind her of him.
Megaton Punch - The use of Solty's Power Fist.
The Messiah - Solty.
Mid Season Wham Episode - The "death" of Rose, just after she is revealed to be the daughter Roy has been looking for all along.
Motor Mouth - Solty, too.
No Transhumanism Allowed - Averted. The series is full of cyborgs and genetically altered individuals.
Parental Abandonment - Done for a good cause by Rita "Ravant's" father.
Playing Against Type - Joji Nakata, a hero?! Whoa.
Police Are Useless - They don't even investigate attempted murder unless you come file a report.
Powered Armor - The RUC team.
Power Glows
Power Fist - Solty, when it starts vibrating.
Really Seven Hundred Years Old - Solty, Ashley and Joseph
Robot Girl - Initially assumed to just have a lot of cybernetic enhancement, Solty is revealed to be one.
Roof Hopping
Rummage Sale Reject - Solty picks the... unusual outfit after Roy says he "loves it" without looking at it just to get her to pick an outfit.
Sadistic Choice - In the Grand Finale, Roy is being forced by Ashley to choose between Rose and Solty, both captured. Roy takes a third option and shoots the tentacles launched at him. Ashley shoots him instead and a very pissed off Solty frees herself.
Shoot the Dog - When Larry Anderson is involved, criminals don't survive the day.
Small Girl, Big Gun - Kasha, when she grabs and fires a giant bazooka.
Spirit Advisor - Will serves as a sounding board for Solty's introspection.
Taking the Bullet - Both Roy and Solty have done this. Comes out better for her than for him. Solty actually catches a bullet, carrying the momentum into a backfist on the attacker.
Theme Naming - The RUC girls are all named after Japanese cars. The three Master Computers are named for the Greek goddesses of law and order, the Horae.
Unusual Ears - Solty's are long, pointed, expressive, and the same color as her hair. Kasha actually asks if it's some sort of new fad.
Unusually Uninteresting Sight - Rose holds Roy at gunpoint in the middle of a busy sidewalk, and no one but Solty reacts.
We Help the Helpless -- Rose and her partners.
Your Princess Is in Another Castle - Episode 23 ends with Ashley and Eunomia defeated, and the city rebuilding, complete with Hard Work Montage. Unfortunately, Solty discovers that Eirene is about to pull a Colony Drop on the city. Not good.