To better explain my choices from the prior top five listings, I present them in sections.
Atari 2600 -
Who doesn't like Pitfall? One of the earliest running and jumping games with different obstacles over the course of various screens. Sure the underground was static, but the background of the fores had the number of trees change. However the highlights include lakes, pits, crocodiles, campfires and swinging vines. It also had open world exploration, you could go left or right from the get go.
2. Yar's Revenge
A shooter at the core. Blow away the enemy shield and hit their weak point. Except your ship could collide with the shield and "eat" bits out of it, and in fact had to do that to create the shot necessary to blow up the enemy weak point. And there was a worm-like enemy thing trying to hit you to kill you. You could hide out in a "neutral zone" to prevent its touch from hurting you. The enemy also had a super cannon that would shoot at you from out of their weak point, tracking you to a degree, forcing you to stay mobile. The super cannon shot can kill you even in the neutral zone. Oh, and the instruction manual even had a 6 page comic book in it to explain what was going on. This game was pretty epic in its day.
Speaking of shooters, this one holds a special place in my heart simply because I "flipped the disk" on New Year's day back in 1985. What does that mean? I scored so many points that the game couldn't keep track of the value and reset to zero. Also one of the great-grandfather of space shooters in our day.
4. River Raid
I sure do like shooting games for the old Atari. This one I praise the laurels of being a top-down style shooter with an evolving background track to fly in, with all manner of enemies and even including resource management (a refillable fuel gauge) as your timer for how far you could go and high you could score. It even had a sequel.
Last is my favorite competitive title, what other game has two tanks shooting at one another in a small maze-like arena where their shots can potentially bounce off the walls, the tanks could turn invisible, or you could exploit shooting through corners to hit the other side of the screen?
A few honorable mentions for me are also games like Congo Bongo (another platformer with some complex jumping parts), Pac-Man (Yes, its a lousy port, but the general gameplay was the same and that's all that mattered to me at my age), Defender (Flying, shooting and picking up those always imperiled citizens)
Games to avoid? Indiana Jones and the Raiders of the Lost Ark. (The opening screen seems to have an invisible pit that drops you into a room with an unkillable foe who will eat you if you can't escape, except you can't seem to escape otherwise), E.T. (though I have beaten it, on many occasions, and didn't see what the big deal was about how bad it was) and just about any game that is one screen of static placements versus an onslaught of foes (not Missile Command or Space Invaders, but something like Atlantis)