A pretty old one but a good one: Raptor: call of the shadows. Though I've gotta admit I sort of cheated (level 5 or 6 in the first area gives you an expensive weapon very early in the level. Get to there, grab it, abort the mission, restart...do this about 20 times, then sell all the collected instances of the weapon and get the most powerful weapon to powerhouse your way through the rest of the game).
Also probably a bit dated: parodius. I especially liked that this one - like the name suggests - didn't took itself seriously. While the combination of a hard shooter and a cutesy-looking one was very weird, I have fond memories of playing it.
In the more traditional sidescrooler shooter-genre, I want to give a shout out to 'enemy mind'. It trows far less bullets as you than the average shooter (let alone traditional bullethell shooters), but the main mechanic is very interesting. You're basically an entity that can - and must - capture enemy ships by hitting them with a sort of beam (so you basically have two attacks: your standard fire of the ship you currently posses and that beam to capture another ship).
EDIT: I'll list two more entries, though they're more roguelike twin-stick shooters.
Nuclear throne: pixel-art style game with lots of guns and some upgrades every so level.
Enter the gungeon: haven't played this myself, but looks very similar (it's Zelda with guns, guns and more guns).