From Yukiru Sugisaki, the same woman behind D.N.Angel, comes this particularly bizarre Magical Girlfriend series.

Tomonori Iwaki is in his third year of middle school and is depressed that his teacher, who he's had a crush on, is getting married. He comes home from school, only to be greeted by a young girl calling him "Darling" and suddenly declaring herself to be his wife... and her three secrent agent "dads", who have been assigned to protect her. Of course, it's not a good idea to make this girl angry — her tears contain nitroglycerin and can blow the Iwaki household to smithereens!

Throw in a Love Dodecahedron and a generous helping of comedic mischief (and a fair amount of drama, of course) and that's Rizelmine in a nutshell.

Tropes used:

Adaptation Expansion - The manga was only seven chapters long.
All Love Is Unrequited - For most of the anime, other than the teacher's off-screen fiance, this trope holds brutally — Iwaki has a crush on his teacher, Rizel has a crush on Iwaki, Ryunosuke has a crush on Rizel (or at least on her bear print panties,) Aoi has a crush on Ryunosuke, Kyouko also has a crush on Iwaki... and they all end up happily paired off, one of them with a dog.
A Twinkle in the Sky - Iwaki commonly does this to Rizel, but she seems to enjoy it.
Big "NO!" - In the penultimate episode, in 4 different languages.
Bishounen - Ryunosuke
Calling Your Attacks - Aoi does this in similar way to Captain Falcon. So do the four foreign Rizel wannabes.
Color Failure - Tomonori at his teacher's wedding. Lampshaded by Rizel.
Double Entendre - So many times, abused over the top
Fanservice - Lots and lots, and even more parodies of Fanservice.
Funbag Airbag - Usually by Kyoko.
Gratuitous Foreign Language - The foreigners Lux (English), Rachel (Russian), Lobelia (Italian) and Lan-Lan (Mandarin Chinese).
Hot For Teacher
Humongous Mecha - The titular Rizelmine.
Innocent Innuendo - Again, so many times. Despite the ecchi situations involved, Rizel remains an innocent.
Jerkass - Tomonori is VERY mean to Rizel at first, and gets his comeuppance by her tears.
- Jerk with a Heart of Gold - After his Character Development.
Kawaiiko
Level Up At Intimacy 5 - The handlers of several countries' supergirls try to get Iwaki to have sex with their charges, erroneously because of this trope.
Likes Older Women - Tomonori, which makes his being paired up with Rizel that much more aggravating for him. Which makes the source of his fetish all the more ironic.
Lolicon - Ryuunosuke often denounces grown women, hence a foil to Tomonori.
Made Of Diamond - Rizel
Magical Girlfriend - Rizel, again.
Meganekko - Kyoko, though she doesn't need her glasses to see, but rather to suppress her Superpowered Evil Side.
My Name Is Not Durwood - Rizel never gets Ryuunosuke's name right.
Nanomachines - The supposed source of Rizel's indestructibility.
Non Fatal Explosions - Explosions can destroy walls and objects, but can only do no more than giving people a few singes, and that includes ordinary people with no superpowers.
No Name Given - the "papas" and "mamas" are not given names other than A, B, C.
Nose Bleed - Tomonori's father seemingly has a Lolicon fetish and gets nosebleeds once in a while from Rizel.
Not What It Looks Like - Again, abused over the top.
Older than They Look - Rizel, whose growth was stunted when she turned twelve as a complication from the technology involved with her creation. Before the technology reverted her to the young waif she is in the anime, she was quite an mature-looking babe — guess where Tomonori's fetish comes from?
Once per Episode - In the anime, Rizel cries at least once by the end of the episode.
Pair the Spares - This is how a number of the issues of the Love Dodecahedron are resolved. Ironically, this includes a dog.
Panty Shot
Porn Stash - Subverted. Rizel dressed up in Hadaka Apron which she said comes from pictures in what apparently Tomonori's Porn Stash, but it turns out it is his father who hid those pictures in Tomonori's bookshelf.
Rape as Comedy - Aoi's relationship with her boyfriend/dog could be described as this.
- And Kyoko too, with with her glasses off.
Screw the Rules, I Make Them! - Rizel is so important to the government that they bribe Tomonori Iwaki's parents to let Rizel stay. Then they make her marriage licence (which was filled out without her "husband's" permission) stick, and fly her to Mt. Everest so she can get a apology gift.
Shout Out - Sometimes the characters mentions other anime and fictions, such as Doraemon and Steel Angel Kurumi. Lux also drove the KITT in Knight Rider.
Stalker with a Crush - Ryonosuke and Kyoko.
Token Mini-Moe: Sweet little Rizel.
Tsundere - Tomonori is a male Type A towards Rizel — ironically enough voiced by Rie Kugimiya, who was soon to get typecasted into voicing a lot of Tiny Tyrannical Tsunderes, starting off with Shana.
The Vamp - What becomes of Kyoko if she loses her glasses.
Verbal Tic - Lan-Lan with her "de aru" and Rachel with her "-ski".