Amusingly, the show is absolutely crammed with shout-outs to other series/franchises.
The producer of the series, Akio Mishima, has come out on record as saying that much of the series was inspired by Nanoha's "Gundam-ish" concept art, particularly the staff and the colours of her uniform (Nanoha tribute fanbook, in Megami Magazine #91).
And the shout out was returned in Gundam Build Fighters, where way the Star Build Strike's Discharge System works suspiciously resembles the Starlight Breaker.
Fate also gets a major shout-out in the form of her Intelligent Device's sword form - a black sword with a trident-shaped hilt. That extends for MILES.
In StrikerS, Signum is often accompanied by a red-headed nun with wind-based magic and a similar fighting style to Axel Almer. Lamia and Axel both debuted in Super Robot Wars Advance, where they were rivals. It gets more hilarious that when Axel gets into the spinoff game Endless Frontier, he fights on foot... with that red-headed nun's weapon - a bladed tonfa, and the ability to create tornadoes.
In Force, to add up more Signum-Lamia comparison. Signum gets curb-stomped and nearly killed off by newcomer Cypha of Hückebein through cheating. Comparisons could be drawn between Cypha and Wilhelm von Juergen, the "newcomer" in SRW, who debuts by capturing, humiliating the hell out of Lamia and presumably killed her off (temporarily), through accidental exploitation of Lamia not being in her mech, in other words... accidental cheating.
While this is less of a blatant one than the previous one, maybe you should give Zest Grangeitz a look. Now imagine what happens when you give Sanger Zonvolt, The Sword That Smites Evil! brown hair... see what I mean?
SRW has started giving NanohaShout Outs back - in SRWZ, the Balgora Glory's attacks suspiciously resemble Nanoha's.
In fact, several of the characters are schoolgirl-shaped versions of various mecha. Nanoha herself is such an expy of the original RX-78-2 that she appropriated its nickname "The White Devil", which is now more associated with her than with the mecha in some circles. Nanoha uses fin funnels during the third series due to the standard powerup curve making her resemblance to a Gundam of the later UC timeline even more pronounced.
Meanwhile, her Revolver Knuckle and her sister's name are references to Gear Fighter Dendoh, while the physical appearance of the sisters, particularly hairstyle and ribbons, recalls Noriko and Kazumi, the pilots of Gunbuster, which happens to have spiked rollerblades built in.
Reinforce, and her tinier, cuter incarnation, Reinforce Zwei. In Victory Gundam, there's a battleship named Reinforce, which was later remodeled into the Reinforce Junior.
The second episode features an Expy of Ein from Cowboy Bebop being possessed by a Jewel Seed.
Teana's weapon, Cross Mirage is named after a mech from The Five Star Stories & its design appropriately has a slight Mamoru Nagano vibe to it.
Not an anime shout-out, but the A's in Nanoha A's is a phonetic sound-alike of "Ace," and that season also features the first appearance of "Belkan Knights," who utilize a triangle array in their magic. In Ace Combat, the Belkan Air Force uses a triangle as its emblem and is rooted in the traditions of the ancient orders of Belkan knights.
Fate's Bardiche has a whole heck of a lot of Shout-Out metamorphoses.
The scythe form being called Ha(r)ken comes to mind.
The Zanber Form bears a distinct resemblance to a Zankantou.
The Riot Zanber Stinger form bears a striking resemblance to the weapon used by Shelke in Dirge of Cerberus.
Thoma makes a "contract" with a mysterious girl being held captive. His left eye starts bleeding, then he transforms into a being called "The Black Knight" and casts a spell called "Divide Zero". Code Geass anyone?
Jail Scaglietti looks like Ingram Plisken. A technical genius who brainwashed two heroines into fighting for him, created an Opposite-Sex Clone of himself as an assistant, was later cloned further, and eventually betrayed his masters.
Lutecia's summon, Garyu, is an insect like humanoid monster with a similar design to a Kamen Rider. To add to this, its arm can form a blade similar to the one Gils can form, has a Scarf of Asskicking and, in a fight with Erio, kicks in a very similar way to a Rider Kick.
Vita's hammer can take on a form that is a reference to GaoGaiGar and another which references Gurren Lagann with a drill on the front. TTGL aired in the same season as StrikerS and the hammer is voiced by the same Japanese VA as Simon. Appropriately, that season showed Vita to be a Determinator like everyone's favorite Hot-BloodedGurren Lagann protagonists.
Look at this guy from the new Force manga. Now, go play Final Fantasy VIII and take a look at Squall Leonhart. No, you aren't hallucinating, they really are a scar and a bottle of hair dye away from having basically the exact same character design.
The similarities become more pronounced when you realize that he uses a GUNBLADE.
The Numbers's outfits suspiciously resemble plugsuits from Neon Genesis Evangelion, right down to the wristcuffs, shoulder armor things, and hair ornaments.
The Council is also a big and very blatant Shout-Out to Evangelion: the three big screens with "Sound Only" and the fact that the council is composed of three ArtificialIntelligences that are basically three big brains in glass tubes.
Sein's IS ability is called Deep Diver - it allows her to swim through solid objects. This bears a striking resemblance to the ability shown by Ms. Deep from Read or Die.
Cinque wears a Badass Longcoat and has the ability to charge throwing weapons with explosive energy, similar to Gambit.
Her eyepatch, combined with her trenchcoat (which actually gave her stealth ability) makes some fans compared her with Big Boss.
Much like in Macross, The Movie of the first season actually is an in-universe movie produced on Midchilda.
In A's, Hayate Yagami has many similarities in appearance to Lain from Serial Experiments Lain most obviously in the form of her hair ornament, but with other, subtler examples.
It's somewhat ironic that Signum shares a voice actor with Lain.
Vivio's friend Rio in the ViVid manga has a pair of spells called Enryu and Rairyu that conjure up twin dragons of lightning and fire. The spells are obviously named after EnRyu and RaiRyu of GaoGaiGar fame, and when both dragons are used together the resulting attack looks virtually identical to GekiRyuJin's Xiang Tou Long attack.
In StrikerS, certain characters are given "limits" on their power that, with approval, they can release in order to power up. For most of the series, doing so is merely referred to as "releasing your limit", but in one episode, Nanoha specifically talks to Hayate about using her Limit Break, with "Limit Break" said in Gratuitous English more than once.
Vice Granscenic is a Friendly Sniper whose greatest failure was accidentally shooting her little sister with his rifle and as a result, he couldn't shoot a gun anymore. He gets his touch back for the final battle, however. This Troper can't help but compare this character to Al Powell from Die Hard who accidentally shot a kid with a plastic gun but eventually got his skills back when he kills The Dragon in the first film.
In ViVid, there are two competitors named Harry Tribeca and Vitoria Dahlgrün. Harry is a delinquent who uses fire techniques with her signiture attack named "Gun Flame." Victoria, on the other hand, is a refined lady who uses electric attacks. Both consider each other as rivals. Kinda reminds one of Sol and Ky doesn't it?
The series also packs a reference to the Cthulhu Mythos of all things with the the Precursor civilization being named after the author of the Necronomicon.