Wow this seems like the place.
Anyways, I have two games that I remember playing all the time. I played them on a knockoff console (plug in and play type), which was a very direct and blatent rip off of the purple N64 controller, but had a a battery pack at the back (springs and all, in a purple case), detachable with a button, and a serial port, which you can connect another knockoff controller to. It played NES games, such as Magmax (the NES port), kung fu, snack attack, balloon fight etc, so I assume that the game that I am thinking of was on the NES. I'm not sure if all of the games were exclusive to the NES ports.
The first game is a top down shooter, where you are a ship/plane/jet and have bombs and a standard attack. The bombs can be used to destroy ground buildings (kinda like xevious), but only if your ship hasn't been shot once yet. The ship can take a total of two shots, first one removes bombs and also turns the music into a slower sad tone, while the second one destroys. If you play with two players, you can merge the ships at the wingtips if done perfectly (otherwise it bounces off. The combined ships are played by the first player, and fires two shots. There are bonuses in the form of large diamonds (which probably appear after killing an entire group of enemies, which if left to collect, they speed up towards you, and just give points. The diamonds can also be shot multiple times, every now and then changing colour, to offer different bonuses. Sometimes the diamond darkens, and when picked up, it gives a motion blur effect to one ship (probably speeding up movement of one ship (that's the only other power up I remember). There is a boss at the end of every level, which when beaten, advances to another level. The art style of the ships, enemies, stage and boss change in every level. The second level has the ship being blue, I think.
The second game I have no idea if it is NES or not. It is also a top down shooter where you are also a ship/plane/jet, but at the start of the game, you lift off from a runway, with the choice from 10-20 different accessories, each with different types of main attacks. There was one which fired a narrow wave, which goes a short range (kinda like the galaga arrangement for ps2 ship did), and there was also one which hand orbiting black orbs, which could deflect projectiles, if they hit it, perhaps only once, perhaps infinitely. If you were hit with wing accessories attached, you would lose it, and you would be left with a plain ship, which had very little wings. I remember that there was a button to discard the wing attachments, leaving them to flutter off to the ground, and leaving the hull of the ship plain, to perhaps pickup a more preferable set of wing pickups. There were random wing pickups around the level (just like the blue yoshi wing pickups in some levels in super mario world). Without wing attachments, the standard ship's attack would be narrow and short, just like Metroid Samus's orange juice firing blaster, at the start of the game. The bosses were very brightly coloured, and the boss made a very crackly sound, similar to Atari games such as yars revenge. The bosses filled half of the screen, and fired various projectiles. You had to hit strobing weak shots to chip off layers of armour and armaments, and make more atari yars revenge like sounds.
Thanks!