The Million Ton Break-up
100万トンのバラバラ (roughly "The Million Ton Break-up") is a 2010 PSP game with a delightful aesthetic and soundtrack. From the game design perspective, it's interesting for being the most sophisticated variation on Qix ever developed.
The main character is a soldier in a patchwork city, tasked with defending against the waves of unmanned battleships that attack periodically. Where the battleships come from or why they attack isn't clear, but the method for downing them is well established: cut them down to a manageable size and they'll fall out of the sky.
While ships come in a variety of shapes the most common one is a conglomeration of blobby sections connected by smaller spans, viewed from the side. At the start of a stage the player character is plopped down somewhere on the ship, and while objectives vary the most basic one is sinking it by cutting it down to some percentage of its original size. The player can move freely about the ship and can cut normal material (at the cost of slower movement) by holding down a button. When some portion of the ship is isolated by cutting, the smaller part falls off. Here's a quick Let's Play of a stage:
There are lots of complications to the basic idea: some parts of the ships are made of a harder material that looks like dark diamond plate which can only be cut with bombs or while using a special boost gauge; your character moves faster when boosting but they're also much harder to control, so cutting large hard sections requires careful planning. Powerups that charge your boost gauge, stop time, or make you move faster are scattered around, but they're often located in dangerous areas or require clever use to complete the stage. Enemy robots, turrets, and occasionally player-seeking missiles also patrol the battleships, and sometimes you can't cut indiscriminately because you have to save captured comrades first. On top of that if you don't finish within a time limit bombs start dropping near the player at an increasing rate. Overall things get rather hectic.
The soundtrack is also spectacular, featuring a lot of horns, a vaguely martial feel, and even a vocal theme song.
Unfortunately it never got much attention and didn't get release outside Japan; that said, copies are still pretty cheap (<1000円) and it's easy to enjoy the gameplay even if you don't understand Japanese. If you get a chance to play it, do give it a shot. Ψ
EDIT 2022-01-18: More than five years after posting this, and more than ten years after the fact, I realized this was actually released in English as "Patchwork Heroes" in 2010. It did get a few reviews (like this one), but was mostly obscure. It was download only so I assume it is no longer available after the PSP store shut down last year. A pity!