Probably the most iconic and distinctive form of Good Scar, this scar consists of two clean, intersecting cuts that form a cross or X on the hero's face. Generally, it serves to imply that the hero has been through quite a few skirmishes while making them look Badass.
How the hero got such a scar is usually not explained. Part of our brain tells us that getting such a scar in battle is highly unlikely, if not impossible (unless they're deliberately inflicted, such as in torture). Nobody listens to this part of their brain for more than ten seconds.
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Anime and Manga
The poster child of this trope is Kenshin Himura of Rurouni Kenshin fame. The cross-shaped scar is associated with him so utterly that characters with this scar are regularly accused to ripping the idea from him, even if they predate him by years. Unlike many examples, Kenshin's scar proves to be from two separate incidents. In the anime, the second one was deliberately inflicted so as to make it an X.
Full Metal Panic!'s Sousuke Sagara has had one of these since he was at most twelve-years old (and likely younger). It's origins have yet to pop up, but fanon suspects that they were inflicted during torture.
Humorously, his Bonta-Kun costume has the same scar.
Laboon, a whale, is covered in x-shaped scars from his attempts to destroy Reverse Mountain by bashing it with his head.
After the Time Skip, Luffy also has a huge X shaped scar on his chest. He got it from Admiral Akainu during the war at Marineford. If you check him out while Jimbei is carrying him, you can see it's still fresh.
Tsukune Aono from Rosario + Vampire has a huge one on his chest, among several smaller scars. Got it from a random mook, but it also marks the first time he released his ghoul powers without Moka's aide.
John Hartigan of Sin City: That Yellow Bastard has an X-scar on his forehead.
One Marvel comics character, Agent X, was distinguishable early on for these scars across his face. After being healed of these during a quasi-mystic ritual, he disappeared for a while. When he came back later on, the scars were back; he apparently carved them back on himself!
Cable has one over his eye, although sometimes it's drawn with 3 lines instead of just 2.
Captain Jack Sparrow gets one on his cheekbone in time for the fourth Pirates of the Caribbean movie, though we never get an explanation as to how he got it.
In the latter books of The Dark Tower, Callahan has a cross-shaped scar. It was a memento from two would-be killers, who had tried to carve a swastika into his forehead, but were interrupted.
Redeemed Ulic Qel-Droma, from the Tales of the Jedi series, has this scar on his forehead.
Ripred from Gregor the Overlander gets this type of scar near the end of the fifth book from himself, so he could fill the role of the a person from one of Sandwich's prophecies.
Tibarn from Fire Emblem Tellius has a large one where the horizontal cut extends across his nose and onto his other cheek.
Mega Man X's Axl has one of these. Why, as a robot, he hasn't had them fixed up is never even brought up.
Being who he is, he probably keeps it for the same reason the trope exists. However, it does heal when you use his White Armor in X8.
A common joke among the fandom is that it's self-inflicted, and is essentially the equivalent of tattooing the name of your favorite Bad Ass on your body.
Doumeki Kai of Osu! Tatakae! Ouendan! has this. One wonders where he got it, since he is, after all, head of a cheerleading squad.
Similarly, Elite Beat Agents has Commander Khan. Slightly more understandable, since he was a former CIA agent, but not by much.
Zack Fair of Final Fantasy VII fame has one of these on his cheek. Crisis Core shows how he got it... but strangely it only shows him getting one cut on his cheek.
Inverted in Kingdom Hearts, as Saix has a big ol' X right across the bridge of his nose, and he's not a heroic sorta guy. We later learn that he's been slowly turning into yet another Xehanort host for some time, and Xehanort's obsession with that letter involves using it to brand his "property". This raises some worrying questions about how he got that scar...
Sue from Cave Story has one of these across the bridge of her nose.
Raven from Tekken has the two scars in the middle of his face, meeting above the nose.
Oscar, a sniper from Valkyria Chronicles, sports one of these on the left side of his forehead. He acquired it when he protected his brother in an unexplained incident from when they were children. Musaad, a scout, also sports a similar one in the same place. His scar likely came from his involvement in the previous war in the backstory of the game, him being a famous war veteran and all.
Glenn in Chrono Cross. Due to Sprite Mirroring, it's hard to say whether he has these on both cheeks or just one. And this is only the kid brother of the really heroic knight.
Sir Muir, in the webcomic Harkovast has scars crossing over his right eye.
Hanna has an X-shaped scar, but it's not on his face, it's on the sole of his foot. (He might have one on each foot, it's hard to tell.) X shapes are a motif of the comic in general and Hanna in particular; it's anyone's guess how much of it is related to Hanna's Mysterious Past and how much is just because Tessa likes to draw cross shapes.