OK so we are steadily marching forward in time here and we're now solidly in the bulk of the 80's and even possibly the early 90's (though I'm not sure)
The Atari was fun but eventually it died out and people thought the days of console gaming were over. Along comes Nintendo with Super Mario Bros. which incidentally also launched in Arcades (though it's such a long game I don't that was very appropriate for poor mothers if their kids were good at it and always got the one-ups.)
On top of that Nintendo's console is a smash hit with numerous titles and someone else tried to get in on a piece of the pie, namely Sega with their "Master System".
(Yes Sega, much later on lost the console wars but not until they had fostered some fabulous gems and even after they lost and allied themselves to their old enemy Nintendo they continues to make a mix of really fun (Monkey Ball) and really crappy (later Sonic titles))
So I'll start with Sega's top 5, in no particular order:
1. Altered Beast (2 player): Yes its an arcade port but its great because its a wonderful game and you don't have to pop quarters any more. You start out as a human each time you revive from death, and you have to gather power orbs from killing undead to become a werewolf and kick some serious butt. Simple idea, great gameplay and creativity.
2. Golden Axe (2 player): Similar to Altered Beast except you pick from one of three heroes and try to chop your way through the side scrolling levels without dying. Minimal Mario skills required. Massive axe and sword skills a must though.
3. Choplifter(1 player I think) You control a helicopter and are trying to save people running on the ground and at the same time destroy/or avoid enemy fire from all over the place. Very varied and fun levels.
4.Double Dragon (2 player on most systems)
This was not a Sega exclusive either but was an awesome game and a great complement to their system at the time. Sega had purposely take the "rugged rebel" look and attempted to make it their mantra after all. In Double Dragon, not only is there co-op, there's friendly fire! You can easily get into a fight with your partner and waste all his lives. In fact, the clincher at the final boss of the game is you defeat him and them fight your partner in a battle to the death for the girl. Little boys like me loved this game.
5. For the last entry several titles vied for entry such as R-type and Strider but I'll save Strider for the much better Genesis version, and give the prize to Rampage! (yes the one in the arcade again) Rampage was pure awesomesauce. You got to break down buildings and be King Kong or a Godzilla (Lizzy) If you aren't familiar with the title there is hope for you yet. There is a Rampage title out for the Wii for those who can't get enough and I've played it and it's decently fun to throw cars and destroy buildings in 3D.... or you could just find it in your local pizza parlor if you're lucky ;). (P.s. this game also has friendly fire if you play multiplayer)