Gadgeteer Genius that she is, Skuld of Ah! My Goddess could probably drum up a flamethrower from old engine parts, or a disintegrator ray from a disassembled TV set, but, nope, she relies on bombs. ANDHOW!
Considering that Black Lagoon is essentially the anime equivalent of a Hollywood action film, it should be no surprise that the explosions can get to ridiculous levels at points, especially when it comes to the cars.
The preferred method of dealing with Genetic engineering mishaps in Blood+ is 'Option D', which means dropping missiles on the affected area. On a smaller scale, Kai uses special bullets which ultimately cause parts of Chiropterans to explode.
The title of Btooom! is supposed to be that of the sound a bomb makes when exploding. The story's whole premise is a Deadly Game where the only weapons given are bombs, so there are plenty of explosions.
The "Cowboy Funk" episode of Cowboy Bebop involves the crazed Teddy Bomber; who blows up buildings throughout the episode (the last one nearly taking Spike and the cowboy Andy with it). Jet even states that the reason why no one goes after Teddy Bomber is because they don't want to get blown up.
One Contractor in Darker Than Black was a little boy who could blow up anything he'd left handprints on. This was impressive enough when the results were seen from a distance or when he was just using gravel as cherry bombs, but when he marked everything in the room with handprints? Yeesh.
Dragon Ball Z is made of this trope by the end of the Frieza saga. Planets get blown up left and right.
The final episode of Excel Saga features Nabeshin espousing the philosophy that "Explosions fix everything!", then giving a graphic demonstration: a fused Excel and Hyatt are returned to their original bodies when he dynamites the room they're standing in.
This is the standard response of Louise (of The Familiar of Zero) after she gets magic. And slightly before...
This was her original shtick in previous timelines, she relied exclusively on homemade explosives until one of her teammates complained about stuff blowing up in front of them. So she started stealing guns from the local Yakuza.
In Ranma ½, Akane tries to get some hard-boiled eggs by popping a tray of about a dozen or so in the microwave. It explodes spectacularly, blasting its own door off its hinges with such force, the shockwave knocks Ranma (a powerful martial artist) off his feet and the door itself breaks through the plumbing, flooding the kitchen.
In Robotech: The Shadow Chronicles Ariel has a vision of Space station Liberty being blown up Space station Liberty really is blown up, with blast radius of hundreds of kilometers - wiping out the Haydonite Fleet.
Slayers plays with this a lot. To the point that by the beginning of the second season, as soon as hot-tempered ultra-powerful sorceress Lina Inverse starts chanting her most powerful spell (which usually results in mile wide craters, at least), the other characters are running for the hills and trying to evacuate civilians.
Tengen Toppa Gurren Lagann is particularly fond of filling the screen with explosions. Namely, if something is pierced with a drill, it explodes. The first Big Bad is defeated by getting a hole DETONATED on his torso, and the second one EXPLODES SEVEN TIMES.
And then we have the volcano that spontaneously explodes when Kamina and Simon combine for the last time. The movies had the Chouginga Dai-Gurren-Dan create a Galaxy-sized volcano, for the sole purpose of making it explode seconds later, due to their own pure awesomeness that summoned it in the first place.
When the Dai-Gun Doten Kaizan was destroyed, it was done in parts. First Guame's part, due to the thousands of beams pulled after Gurren-Lagann, then Cytomander's, then Adiane's and finally Viral's part, by a Giga Drill Breaker... all from the inside. Safe to say, the recurring explosion looked fucking awesome, and somehow missed Viral, despite the Giga Drill also hitting him in the head. From below. And he survived being inside a giant mecha that blew up several times.
Zeorymer's Dimensional Coupler Cannon warps space to blow stuff up directly. Its Meioh attack creates a Sphere of Destruction visible from space.