Tyrian

Tyrian is a fantastic and extremely well polished vertical scrolling shooter. It is worth noting, however, that it is highly experimental, and a lot of the qualities that merit this praise are the qualities that differentiate it from the rest of its genre.
Firstly, you do not die in one hit. You have two health bars: one for rechargeable shields, and one for the hull of your ship. This radically alters the entire structure of the game. No longer is it a constant test of endurance where you need to dodge every bullet and enemy. Because of this, as well as the game's famous ship customization, the game is able to be significantly longer (each chapter might as well be its own game otherwise)
Despite the level of customizability, the usefulness of many of the weapons is a clear issue. The weapons are not equally balanced, and (especially on the higher difficulties), many of them simply aren't good enough to be worth using. There is a clearly defined "best loadout" that can be easy to figure out rather quickly. On top of this, due to a lack of in-shop information, it can be very difficult to see the actual differences between shields, generators, and ships. All the ships have different special abilities, but these can be difficult to figure out and usually you'd just want the one with the biggest health bar. Many of the different shields actually have different functions (recharge cost per defensive value), but by the time you realize this, you already have the best generator, so it isn't necessary to even stop to think. As for sidekicks, well, Plasma Storm is available at level 1, and it continues to be the best throughout the entire game (arguably being way too overpowered.) This balance issue may be the only real problem with the game; if it were done again, I'd love to see many different options existing in parallel that all have value and are worth using in their own ways.
While I'm a huge fan of narratives in video games that take themselves seriously (it's a valid form of art, y'know), I am equally a fan of ones that don't. Tyrian's story isn't mindblowing or emotionally enriching, but it's fun and it's funny. Told through collectible data cubes that allow you to read what are essentially emails that your ship intercepts, finding the lore and secrets within it offer a fun challenge for those who care. For those that don't, well, the story is as easy to completely ignore as it is funny. It is rarely if ever forced upon you.