I'll list just the ones recently made that are must haves for the genre fan, and why I love them:
ESPGALUDA - Pure genius of a shooter, Cave at it's best, it's on track to replace Dodnpachi as my favorite manic shooter. Why is it so great? All the usual qualities aside, the game sticks out by it's incredible bullet patterns that really must be seen to be believed. They are *insanely* complex, yet when you play the game, it all snaps into place and if you are willing to look, you clearly see what you should be doing to avoid them. They literally move like they have life on their own - it's just so elegant, and such a stark difference from the crappiness of bullet patterns of some other shooters, like GigaWing, which in comparision just seems to throw those bullets at you at some stupid random patterns (I know it doesn't, but that's the impression you get left with after playing Espgaluda). Then there's the 'Kakusai' mode which is another clever addition to a game that helps both the shooter newbies (slows the bullets down for a while) and experts (extremely important for proper scoring) As in all Cave's games, your weapons are massive, and incredibly satisfactory, and enemies explode just the way you want them to.
DodonPachi dai-ou-joy - Another Cave's masterpiece, but I haven't played it enough yet to tell if I like it as much as Espgaluda. If you've played Dodonpachi (emulated in MAME, Saturn and PS1 versions also exist, PS1 version being an incredibly good port, surprisingly better than the Saturn) you know what to expect - it's just even crazier. Lush mechano-organic background, wicked bullet patterns (so far, they do NOT seem as elegant as those in Espgaluda, but it may be just that I need to give it more time) and crazy, screen filling, energy beaming weapons that your ship is equipped with.
Guwange - Most stylish looking Cave's shooter, and none of their always present qualities is missing either. Technically, it looks and moves a bit simpler than Espgaluda or Dodonpachi Daioujou, but it makes up for it with really, and I mean *really* beautiful looking background and character art. Think 'Spirited Away' but even more detailed! I don't think this game was ever ported to anything, so you'll have to play it in MAME, or hunt down an arcade.
R-Type Final - There are some mixed opinions about this game, but I think it's quality is undeniable, so I'll spend some more words trying to present what I think about it. If you ask me, R-Type Final is Gran Turismo of shooters. It's depth may not lie in fantastic level designs and intristic bullet patterns, and you will often find some of the hardcore shooter fans putting it down because of that, but it has hundreds of different ships, each with their own different weapons and abilities, enemy encyclopaedia (that you unlock peaces of each time you kill a specific enemy ship) Most levels have two or more completely different variations that you unlock in some bizarrely logical way, and the game looks absolutely gorgeous.
An example of interesting stuff present in this game (that some people may not even notice, but you will see just how much effort went into it):
First time you enter it, you begin level 2 in some kind od swamp looking area that partially takes place underwater. When you get to the end of that level, you face off against a boss that can normally be killed, but also has two suspicious looking prongs that move in and out of it. One prong is red and one is blue. If you manage to destroy one of those prongs before you kill the boss, the next time you enter that level (on the next playthrough) you will see that the level has basically completely changed it's visual look. It kinda retains simillar objects and layout, but if you destroyed the red prong, the level becomes a lot more dry, desolated place. If you destroy the blue prong it becomes more flooded and begins to look frozen. If you play the more frozen level and destroy the blue prong again when you reach the boss - the next time you play it, the level will be completely flooded, frozen, and you will play it exclusively underwater. Conversely, if you destroy the red prong twice, the third time you will end up playing on a completely desolated desert. Why this happens? You go to encyclopaedia and see that the boss monster on that level has the ability to somehow change air pressure and humidity around itself
)) Of course, you trigger that ability by destroying red (hot) or blue (cold, wet) prong. Nice, ain't it
The game has lots and lots of crazy detail like that which makes it a lot different from other shooters and gives it a very unique qualities. The huge variety of ships with different speeds and abilities also explains why the level design in places maybe had to be simplified, but unless you are that speciffic variety of a hardcore shooter fan, I doubt you'll hold it against the game, when you see everything else it has to offer.
Take a look at this site,
http://www.slateman.net/rtype/rtypefinal/
It has a master list of all the ships (organized in hierarchy) and explanations how to unlock all the level variations (some secret levels can for example be accessed only with certain ships)
Gradius V - Haven't played it personally, but there's so much praise for this game going on, and it looks just gorgeous. Developed by Treasure, so I guess it's safe to say that if you liked Ikaruga and Radiant Silvergun, you are going to love this as well.