Brawler Lock

Two characters are fighting, and during the course of the battle, they clasped their hands together and push against each other in a test of strength. This can happen when one of them throws a punch or any kind of strike and the other catches it. They can stay like this for a while, with one trying to overpower the other and bring him to his knees.....

A Groin Attack is possible. Also, the combatants need not lock fingers. Grabbing each-other's wrists is also an option.

A combat trope, see Blade Lock for this with swords.

Examples of Brawler Lock include:

Anime and Manga

Dragonball Z did this a few times, with Goku on one side and Freeza, Cell and Vegeta on the other.
Transformers Armada did this frequently.
In Tenchi Muyo!, Ayeka and Ryoko have done this during some of their battles.
In Ranma ½, Ryouga does this with Girl Type Ranma in the last bit of the Golden Pair arc (in the anime at least)
A mecha-sized version happens in GaoGaiGar Final, when Gaofighgar and Gimlet emperor grasp hands. Gimlet thinks he's winning..........but he's fighting Gai Shishio.
During the Edolas Arc of Fairy Tail, Erza Scarlet ends of doing this with her Evil Twin Erza Knightwalker as a result of a Fearful Symmetry induced Combat Breakdown.
Tengen Toppa Gurren Lagann has the Spiral King Lordgenome do this with Simon... while Simon is piloting Lagann. That's right. Genome gets in a mercy-fight with a fucking robot (an admittedly small robot but still bigger than most humans)... and he wins!
- Later in the series, the titular Tengen Toppa Gurren Lagann does this with the Anti-spiral's Grand Zemboa during the final battle.
Greymon did this with a Dark-Tyranomon in the Christmas episode of Digimon Adventure 02.
During the Kanto Season of Pokémon, Charizard and Magmar were doing this. It led to Charizard defeating Magmar in the heart of a volcano itself!!!
Bleach anime episode 220. During Captain Komamura's fight with the Arrancar Poww, Komamura's Bankai (a giant samurai) and Poww's huge resurreccion form grab each other's hands and test their strength. Watch it here.
Rumiko Takahashi's Maris the Chojo does this, between the titular character and her rival Sue. Both are super strong due to coming from a planet with high gravity, but Maris is at a disadvantage since she can't remove the restraints that keep her strength in check.
In the final episode of Yu-Gi-Oh! 5D's, this Yusei fudo's shooting Star Dragon and Jack Atlas' Scar Red Nova Dragon do this when a battle is initiated. Since they have the same number of attack points, both are destroyed.
In Naruto, during their Chunin exam fight, Sakura and Ino end up briefly doing this, along with cross counters, and Punch parries. It slightly different from other examples in that they break away before getting to the fingerlock part.
The Big O episode 17 "Leviathan". The Big O grabs the title megadeus' pincers during their battle.

Comic Books

Marvel Comics did it as far back as The Sixties, when The Mighty Thor first went up against The Incredible Hulk. They've done this many times since. One of the more famous examples was when The Avengers fought The Defenders.
During World War Hulk, The Juggernaut and the Hulk locked up in a similar fashion. The Hulk ended up using Juggy's momentum against him by letting go and allowing him to blast off into the distance.

Film

Obi-Wan Kenobi and Anakin Skywalker do this during Revenge of the Sith, only using Force powers instead of actually clenching hands.

Literature

Someone tries to do this to Bork in The Albino Knife. He lets the guy struggle for a bit, then picks him up and tosses him across the room.
- Later, in Brother Death, Bork finds himself in a similar lock with someone even stronger than him. After several seconds of complete angst, he remembers he's also trained in the universe's most deadly martial art and proceeds to break his opponent's spine.
In an early Discworld novel, the aged Cohen the Barbarian grapples the Luggage (a sapient wooden chest that eats people) to a standstill. Eventually a third party has to separate them.

Live Action TV

In episode 2 of Spartacus: Blood and Sand, Spartacus tries this on Crixus, but Crixus easily sends him flying. Doctore mocks Spartacus' blunder and explains, "Become entangled with a more powerful opponent and you are dead!"

Pro Wrestling

This has existed in professional wrestling for years as the Collar and Elbow tie up, and has been traditionally the way two wrestlers will start a match.
- Besides the Collar & Elbow, this exists in pro wrestling (and many a schoolyard) as the fingerlock, where the opponents lock hands with each other and try to make the other go to their knees.

Video Games

Final Fantasy XI has the downloadable mission pack A Shantotto Ascension, where two Gigantic Shantottos do this, among many other events.
Ultimate Marvel vs. Capcom 3: The Hulk and Mike Haggar do this in the opening cinematic.
This was a mechanic in The Legend of Zelda Twilight Princess, starting with goat herding, moving on to Goron Sumo and finally being used in a boss fight.
- Also used in The Legend of Zelda Spirit Tracks, when Byrne charges up for a rush attack, you can position the phantom guardian/Zelda in front of you, to cut him off, and the two of them will grapple, giving Link an opportunity to attack him from behind.

Web Comics

This Order of the Stick comic has The Hero and Bald Black Leader Guy Roy grappling this way with Dumb Muscle Ensemble Darkhorse Thog. Roy almost wins, too.

Western Animation

An episode of Superman: The Animated Series had Supes doing this with John Corben, aka Metallo. Supes didn't know Corben had been changed into a cyborg with his Kryptonite Factor as the power source, and he paid for it.
In Jackie Chan Adventures, Tohru and El Toro do this in El Toro's introductory episode. What with them both being wrestlers (sumo and lucha libre, at least), it was probably inevitable.