Gradius - Lifeforce - Jackal
All three of these games were developed by Konami and encompass what I call the Konami Shooter Trilogy. Unlike Japan, the US did not receive a version of Gradius 2 or Parodius, but Europe never saw Jackal either. I note that Stinger was also released by Konami, but while it is a fine game in its own right I do not consider it to be in the same league in terms of popularity or adolescent-focused pure shooting action as these games.
All three of these games began life as arcade machines. Gradius received a very faithful Arcade-to-NES port, although it lacks a bit in the flash and polish department. Jackal is also arcade-faithful as well, but Konami truly excelled here at bringing the fast-paced destruction of this game to the less capable hardware of the NES. Nothing essential is lost in porting. In fact, the game is substantially improved by end-level bosses and level transitions. As I mentioned elsewhere, Life Force is in certain respects a better game than its arcade original, Salamander.
Of course, I cannot go without mentioning the two player simultaneous gameplay of Jackal and Life Force. Two-player simultaneous gameplay was somewhat uncommon in the days of the NES due to the hardware limitations. 64 sprites get used up very quickly, and the 8 sprites per line limitation of the NES leads to flickering very quickly. Konami was one of the few developers who consistently could do it right with Jackal, Life Force, Contra and Super C.
Zanac - The Guardian Legend - Gun+Nac
Here we have the Compile Shooter Trilogy. Zanac and GunNac (note the similarity of the names) are similar in that their basic gameplay model is that of the vertical shooter. The Guardian Legend combines vertical shooting stages with exploration-style bird's eye view stages like The Legend of Zelda.
Zanac has three principal strengths. First, it has a wide variety of powerups (eight) that have their own strengths and weaknesses. Second, it has very solid gameplay, especially for a somewhat early title. It is a fairly fast paced game, the controls are very responsive, rapid fire is present. Even though it lacks varied bosses, it feels very modern. The graphics are good and the music is excellent. Third, the game adapts itself to the power ups you choose and reportedly your skill level. It is not simply a randomizer, the game will behave in somewhat predictable ways, in terms of the enemies it will throw at you, based on the active weapon powerup you possess. This mechanic makes it never quite the same game twice. You can continue at the last area by pressing start and select at the same time on the title screen (this is in the manual).
The Guardian Legend tweaks the formula quite a bit by adding overhead exploration. You collect chips to buy items from the Blue Landers, fight bosses in special rooms and collect keys to open "corridors" to vertical shooting stages. Your character is not just a ship but a female android (which the US version took some pains to obfuscate). It has a password feature for restoring your game, and it is pretty long by NES standards. There are several themes to individual areas, like water, plants and mountains, and the graphics change accordingly. The music is some of the best on the NES. Shooting stage bosses are varied and some are really tough (blue Optomon will make you throw your controller against the TV screen) and others are much more reasonable (even the red Clawbot and Bombarder are reasonable). Finally, you gain many weapons and you can switch between them as often as you like, but you use up chips by using them. Fortunately, the game is fairly generous with supplying you with chips and health items when you need them. By inputting the password TGL, you can play the game as a straight shooter.
Gun+Nac is as to Zanac as Parodius is as to Gradius. Unfortunately, Gun+Nac is not as well-known as it deserves to be because it was released rather late in the NES's lifespan. Gun+Nac plays like Zanac with more powerups. You still collect the Compile "P" chips, but you also collect money so you can upgrade your ship and buy extra lives during the levels. GunNac is cute and goofy with rabbit and cat enemies, but do not let that fool you into thinking the game is a cakewalk, it is not. Graphics and sound are excellent.
Golgo 13: Top Secret Episode - The Mafat Conspiracy - WURM: Journey to the Center of the Earth
Golgo 13 and its sequel the Mafat Conspiracy are a logical choices because they use the Golgo-13 character, but WURM? It is not as far fetched as you think. Golgo 13 advertised multiple styles of play. First, there are side-scrolling areas with some platform (enemy bases) and some free form (underwater) elements like Super Mario Bros. Second, there are first person, 360 degree mode instances where you have to kill all the enemies that are ambushing you. Third, there are horizontal shooter stages when you fly a helicopter. Fourth, there are first person maze stages with traps, items and enemies to shoot. Finally, there are dialogue and cinematic sequences when you charm the ladies.
The Mafat Conspiracy has more of the same, mostly. In exchange for the horizontal shooting mode, you get a driving mode that looks very close to Rad Racer. There is also a more involved sniping mode and the game is much more cinematic overall. The mazes are still as annoying as hell, but in the manuals for both games there are maps. Also, the platforming stages are still a bit stiff in terms of your character's control scheme but there have been some improvements from the first game. One big one is that now button B shoots and button A jumps, it was swapped for Golgo 13.
Golgo 13 and WURM share the same designer, Shoichi Yoshikawa, and he acknowledges that he took inspiration from the earlier game. He even made a direct reference by including the "G-13" robot in the game. However, WURM has an unfinished feel to it that cannot be said for the Golgo-13 games.