Gradius. If you don't know the series: Google is your friend. The Gradius (Nemesis in Europe), and their Parodius parody series has always been fighting with the R-Type series for the crown of shoot-em-ups. I have always preferred Gradius, but that's personal I guess. :)
Gradius V, after having been delayed several times, finally came into my possession a few days after its release in Europe, and it was worth the wait. This game is simply the best shoot-em-up available to date. Take the typical Gradius playing style, and add beautiful 3D graphics (the game is still in 2D though), some very nice music, and a two player mode (both ships flying at the same time), and this game simply couldn't be better. They've decreased the hit area to a small part of a ship, so no more feeling you've been cheated when you die: trust me, you've been hit this time!
As you play the game you unlock more credits to play with, until finally you receive unlimited credits. Combined with the "continue where you die" feature this Gradius packs, and the ability to pick up your options (again, Google if you're not familiar with the typical Gradius terminology) when you die, and the game should be finishable for players of every skill. Luckily I didn't need more than 5, though I've been completely outclassed by several players that have managed to play through all levels of this game several times without using more than a single credit. I'd say the game is just slightly less difficult than Gradius IV.
If you like shoot-em-ups, then get this game. For the moment, it just doesn't get better than this!