To the ones I posted on the post Crooked Bee linked to (
this one) I would like to add the following ones:
Crimson Clover, which just came out around new year, at C79. It's hard and it's quite cool, and it isn't a
cute 'em up so it's a bit more Codex Compatible. It's also quite hard, and given many patterns are aimed at your position and then spread if you move about randomly and with bad timing you can get cornered as several patterns get aimed at diferent parts of the screen in such a way each pattern closes the openings in the previous one.
Witch in Wonderland, next, is kind of a Touhou clone. It's colorful, is cute, is really kawaii, and has very good music (the final boss' song is both awesome and weird at the same time). Also, it has both an HP and MP system, a level up system based on your score, you can change the element of your base attack, and it gets nightmarish from stage 4 onward.
Then you have
Ether Vapor. It is pretty unique in that not only do you have a shitload of different firing modes on the same ship but the game switches gameplay modes on the fly: You start a level doing vertical scrolling shooting, then you switch to sidescrolling shooter, then you get a scene in which you must target missile swarms or fight a mothership in a rail shooter kind of way, then you end the boss fight with an after burner fly by of the boss. Is pretty awesome. It has been translated, too, so you can actually understand the horrible excuse plot, if you are into that.
For Mame, now, add
Storm of Progear and
Giga Wing. Also, for X-Box 360 add
Death Smiles II, which isn't as good as the first one but still awesome and better than most shit out there. And, contrary to the original Death Smiles, has one (almost) Tranny, so it is actually far more Codex Compatible, even if both are so very lolicon you want to cry. For either PS2 or Xbox, meanwhile, add the ESP Galuda (
ESP Galuda,
ESP Galuda II) games, which are spiritual sequels to ESP Ra.De. And ESP Galuda actually allow you to play with two of Esp Ra.De characters, who play completely different to ESP Galuda ones, on
Arrange mode.
Since we went kind of full Cave i'll also add
Eden's Edge and
Eden's Aegis, which are two freeware vertical shmups heavily influenced by Cave, by Blue Wish Resurrection's maker. Also,
Stella Vanity, of which only a Demo exists, and it is awesome even if it is rumored development was canceled.
Those, plus the ones on that other post linked to by Bee, should get you started.
Edit:
Also check the Shikigami No Shiro games,
Shikigami No Shiro III in particular, but keep in mind english translation is horrid in those that has been translated. Also, check 3's varios releases, as one allows you to play it kind of like Imperishable Night or TWAIN, with two characters you switch on the fly, while the PC one doesn't.