Panty Fighter: Lampshaded during the Mahora Budokan. When Asuna and Setsuna change into their provided combat attire they discover after they are already into the sexy lingerie. They have no real choice, so they go into battle as combat maids.
Asuna: I can't do anything in this without flashing the entire crowd!
Panty Shot: Often and Asuna is usually the victim. This reached new heights during Mahora Budokan. See Panty Fighter.
Beside the obvious examples of Negi and Asuna, both orphaned, nearly all the characters live alone in a boarding school with no parents in sight. The two dads that showed up were extremely plot relevant.
Then there's Kotarou — apparently any half-youkai where he's from will be abandoned at birth.
Parental Incest: No actual incest occurs, but Yuuna really loves her dad. She says that she wouldn't mind giving a "deep, passionate kiss" to her dad, which elicits a "No. Just... No" Reaction from Ako.
Party Scattering: The main cast is at a Gateport, having just arrived in the Magic World from Wales. The Bad Guys pick that moment to launch their attack on the Portal Network to cut the Magic World off from the real one. As the system explodes, there's all kinds of swirly craziness and the cast end up scattered in ones and twos across a surface area nearly a third that of Earth. It takes an interminable period to get everyone back together, but when they do, everyone has, as they say, taken a level in badass.
Perspective Flip: A flashback near the end of the final Negi/Fate fight shows us the Lifemaker observing Nagi and Ala Rubra twenty years ago. Rather than being dismissive of the foolish humans, he or she actually seems pleased and respecting of Nagi as an exemplar of humanity. This puts Nagi's final beatdown of the Lifemaker shown in Godel's flashbacks in an entirely different light.
Perverse Puppet: Chachazero has a bit more free will than a normal old puppet, but she is definitely psychotic. In the most adorable way possible.
Playing with a Trope: One of the big reasons this series is so popular is because Akamatsu goes out of his way to toy with tropes common to the Shonen genre and winds up coming up with twists and turns that catch even his own long-time readers by surprise, to say nothing of the people who were expecting this series to be little more than "Dragonball Z meets Harry Potter / Love Hina". See Beam-O-War for one example among many.
Poor Communication Kills: If Chao or Fate would have taken the time to explain their goals to Negi rather than opposing him from the beginning without explaining why, everybody could have saved a massive amount of time and effort. Chao was likely doing this intentionally.
Powered by a Forsaken Child: Asuna powered the magic-cancelling defense system of Ostia while bound in chains as a child. Later she was used to power the magic-cancelling spell that would have destroyed the whole Magic World. Thanks to everyone's joint effort at containment, only the whole of Ostia was destroyed. The resulting mental trauma from being used as the power source to destroy a whole country was probably one of the reasons Nagi and party decided to wipe her memory.
Power Levels: In the manga's Magic World arc, Jack Rakan, with his own personal ranking chart, puts a major villain's power in context with an oddball list that includes: a cat (0.5), a normal human teen girl (1), a tank (200), a magic teacher (300), Negi (500), a dragon (650), an Aegis Battleship (1500), and the villain (3000). Meta Girl Chisame doesn't even know where to begin in pointing out all the problems with such an arbitrary list (which probably shouldn't be taken very seriously.
Power Perversion Potential: Some of the cast are more aware of this than others. Rakan uses his speed and power to flip girls skirts and take their panties off before they notice. His "secret ultimate technique" is Silent Flipping and Stripping, Combined with the Rakan Gentle Breeze Tempest Fist, oddly enough it actually works as a battle strategy.
Princess In The Mountain: Asuna's general situation until Nagi came and rescued her. Later, she goes back to the "mountain" for a hundred year sleep.
Projectile Spell: The functionality of the light-elemental Sagitta Magica attack spell is very similar to your standard Magic Missile. Other-element variations have more varied effects.
Put Them All Out of My Misery: The Fatettes contain aspects of both type three and four, having been wronged (they're all war orphans or worse) and deciding they're going to fix society by completely redoing it. Whether they like it or not. As it's rather bluntly stated to Ala Alba, they at least don't even care what Negi's plan is or if it will work because they're more concerned with making a peaceful world than saving all the people. Having the people saved is a nice bonus to them.
Rain of (Magical) Arrows: There doesn't seem to be a limit to how many Magic Arrows you can shoot off, although it's usually a prime number.
Razor Wind: Wind-type spells, including Negi's old standby Jovis Tempestas Fulguriens, run on this trope. Griffins also have Razor Wind breath.)
Reality Ensues: In a flashback, Tsuruko (Motoko's sister from Love Hina) says that contrary to all shonen logic, someone who follows swordsmanship with no thought other than causing chaos and bloodshed really will become incredibly strong. While Setsuna will presumably win eventually, you can see that this is indeed true during the current fight where Setsuna is getting utterly stomped due to Tsukuyomi's powerups. One of those powerups, incidentally, is one that Akamatsu specifically noted as being one inherent to shinmeiryu swordsman and basically boils down to Tsukuyomi tapping into the dark side and shows up as her Black Eyes of Evil. Setsuna has never shown this powerup before even though other good characters like Touko have.
After Negi starts to crack after one of Fate's speeches, Asuna gives Negi her own The Reason You Suck Speech, the point being that he's an idiot for even considering what Fate is saying. The next time Fate attempts one of these, he gets a punch in the gut and a Shut Up Hannibal for his trouble.
Evangeline has a knack for these, against Setsuna, Asuna, Negi...
Red String of Fate: Lampshaded in one of the first two OVAs: Nodoka and Yue find a spell in Yue's Artifact that seems to indicate who the caster's tied to. Instead, it just ties things together with magical, glowing red string that can't be cut. Since Nodoka was thinking of Negi when she cast it... Hilarity Ensues.
Relationship-Salvaging Disaster: During several years, Setsuna distanced herself from her childhood friend Konoka due to feeling ashamed of her failure to save her from almost drowning when they were kids. In the Kyoto arc, Konoka is kidnapped and Setsuna helps to save her. After that and Konoka telling Setsuna that her wings are beautiful, they become close again.
Robe and Wizard Hat: Most noticeable in Yue's Pactio outfit, which is practically the essence of this trope. Very noticeable when she summons her item while in a 1-piece swimsuit — yes, 1-Piece Swimsuit, Cloak and a Wizard Hat.
Robosexual: Teased at. Chachamaru has obvious feelings for Negi and feels an equivalent to sexual pleasure, but the idea of making a move on him doesn't even seem to occur to her. As far as being 'anatomically correct' goes, she refused upgrades several times.
Robot Maid: Evangeline's resorts are staffed by older (but younger-looking) versions of Chachamaru, usually referred to as Dash-Chachas or Chacha<number>s.
Roof Hopping: Chao, in the chase that sets up the plot of the Mahorafest mega-arc.
Even then it mostly holds up enough that Negi is extremely surprised when Tsukuyomi laughs her ass off when he notes that she's probably working for the bad guys for a noble cause like all the other villains and explains that she's really just playing along with Fate for the opportunity to hurt/rape/kill people. The only other example is the Megalomesembrian senate, who are probably, given the usual lightness of the series, not horrible individually(just selfish and arrogant) and are more just evil through mob mentality.
The entire Magic World arc could count, as the plot is decidedly on the Final Fantasy end of the spectrum, and an enormous number of videogame terms are used to explain the mechanics of how magic works. Not to mention the fact that the Magic World is implied to be a massive artificial reality game, complete with a Game Breakernote and is referred to as such by the characters themselves, and a Big Bad who can literally rewrite the "code" of the "game".
Rule 63: An odd canonical example played for laughs or fanservice with Negi during the Mahorafest Arc as a joke by the class to bring in more customers. Played far more serious with the introduction of Sextum in the Magical World Arc, herself Rule 63 of Fate.