Lightning Glare

The atmosphere between them is charged with tension.

When two rivals (usually but not exclusively female) lock gazes, growling at each other but not yet at blows, the intensity of their mutual loathing is so intense that it manifests as crackling streamers of lightning arcing back and forth between their eyes.

Anime & Manga

Naruto and Sasuke in Naruto. Sakura and Ino as well.
Grandis and Electra on Nadia: The Secret of Blue Water.
Pictured above, Ryoko and Ayeka in Tenchi Muyo
Mahou Sensei Negima
- Ayaka and Asuna, frequently. In Negima!?, it's bad enough to seriously injure anyone that get between them.
- Also, Anya vs. Ayaka, in chapter 180.
Tamami and Buchou in Mahoraba.
In one episode of Inuyasha, Kagome explained the concept of family reunions to Inu-Yasha. He imagined what such a thing would be like for him. Cue a picture of Inu-Yasha and Sesshomaru exchanging a Lightning Glare over sushi.
Cardcaptor Sakura
- Though not specifically rivals per se, Shaoran Li and Touya Kinomoto Lightning Glare at each other more than once.
- Also between Shaoran and Kero.
Happens between Ran and her rival in the opening of Super GALS!
Happens on occasion between Rei and Usagi in Sailor Moon.
Moka and Kurumu exchange this in episode 6 of the Rosario + Vampire anime as Kurumu gives Tsukune a heavy dose of Marshmallow Hell.
In Mr. Fullswing, Saruno and Kotetsu do this in an early chapter, and Saruno uses the sparks to grill food.
Happens between Ikki and Buccha in Air Gear. It starts out as Ikki giving ramen to Buccha, seemingly innocent... Until onlookers get hit by their killing intent, apparently creating an illusion of them being on fire and words appearing behind their backs.
When Vita and Signum get into an argument after Signum reprimands Vita for throwing her clothes on the floor of a public bath in the first A's Sound Stage of Magical Girl Lyrical Nanoha, the viewer can hear them shooting lightning glares at each other.
More than a few times on Fruits Basket. Nine times out of ten, it's Kyou and Yuki.
Words Worth: Sharon and Mew exchange one upon realizing they've each slept with Sharon's fiancee, Astral and that they both have feelings for him.
D Gray Man: Occurs repeatedly between Allen, who can normally get along with anyone, and the notoriously grumpy Kanda. Even their golems get involved, with Timcanpy and Kanda's golem also engaging in a crackling glare contest of their own as they hover over their respective masters' heads. Until Timcanpy just goes ahead and eats Kanda's golem.
Ukyō and Shampoo in the Ranma ½ animated version.
Yurika and Megumi from Martian Successor Nadesico.
Bleach: Retsu and Mayuri do this once in the anime.
In Yu Yu Hakusho, Kuwabara does this to the enemy team leader in the first round of the Dark Tournament.
Ed does this to a bottle of milk (!) once or twice in Fullmetal Alchemist.
Sakuragi and Rukawa in Slam Dunk.
Done by Nagi Sanzenin and Ayumu Nishizawa almost every time they meet in Hayate the Combat Butler.
Chizuru and Nozomu do it to each other in Kanokon, while rubbing against a passed-out Kouta.
A 3-way version happens between Houki, Cecilia, and Rin in Infinite Stratos during a lunch date with Ichika.

Literature

From The Lord of the Rings:

[Denethor] turned his dark eyes on Gandalf, and now Pippin saw a likeness between the two, and he felt the strain between them, almost as if he saw a line of smoldering fire, drawn from eye to eye, that might burst suddenly into flame.

Live-Action TV

The Brazilian comedy show CQC uses this as a comedic, computer-inserted (obviously) cliché every time they ask embarassing questions to the people they interview, and they glare. Of course, half their special effect clichés are anime related...
In Chinese Paladin 3, the two male leads have one of these after simultaneously pushing each other's Berserk Buttons. Played for comedy in this case, because neither actually wants to admit the loss.
In Kamen Rider Fourze, Sitcom Archnemeses Yuuki and Miu engage in this from time to time. Gets a lampshade in episode 5 when another character asks how long they plan on keeping this up.

Pro Wrestling

Sting and Jake "The Snake" Roberts do this in the promotional mini-movie hyping their match at Hallowe'en Havoc 1992.

Web Animation

One of the tropes parodied in the Weebl and Bob episode "hentai".

Web Comics

Buttlord GT takes it to another level, with Kevin and Snowflake projecting dotted lines from their eyes, which create a little explosion when they meet. For however small the explosion is, it's intense enough for Brad to deem it "the sweetest thing ever".

Western Animation

Teen Titans
- Although more of an Eye Beam Glare, Cyborg and Gizmo do this once.
- A better example would be Robin glaring at Starfire in the origin episode "Go!"
- And Robin and Cyborg did this during "Divide and Conquer".
In Wakfu season 1 episode 5, this happens shortly between Sadlygrove and Evangelyne while they disagree on the best way to defend the village.
In X-Men Evolution, as Storm and Mystique glare at each other, actual lighting flashes across the skies in the background because Storm's just that pissed.