PAPERBOY

They don't make them like they used to. Ok, not true, but still - 80s and 90s are replete with oddities that made your usual genre of preference a unique gaming experience. Paperboy does exactly what it says on the tin, and not only will it cater to those Generation Xers who knew exactly what it meant to flip a burger or deliver newspapers to "learn to appreciate the value of money" and afford a new 8bit or 16bit gaming system, but it will also appeal to Millenials, and not just to those Millenials who  search for gaming document of days gone by.

The premise is simple- a paperboy has to deliver his round and throw papers to as many houses of subscribers without being bit by dogs, or hit by a myriad of moving objects, cars, carts, raving neigbours, breakdancers, toys  etc. With some time needed to get acquainted with controls and the scrolling, it plays well and you slowly grow to like evading death traps while trying to keep Daily Sun's readers happy. Even if you do get fired , you get fired to an awesome soundtrack playing in the back.

One can easily of a counterpart from the 90s it inspired. Less death and less guns , though.

And, uhm, don't play the Commodore 64 version , it's really bad.

CHO ANIKI- Kyuukyoku Muteki Ginga Saikyou Otoko

The Japanese call such games "idiot games" and "s++t games", and this series is so utterly nonsensical and original  in its content and visual identity  that you quickly realize there is no other game (series) like it.It is the bizarre combination of many elements that make this classic horizontal scrolling shooter a unique gaming experience. There's  homoeroticism everywhere, the media-perfect oiled male physique that  you were bombarded with as a kid during the 80s and that confused you greatly during the 90s ("wait , I loved He-Man, does that make me gay?", that type of stuff ).There's the surrealism that transcends kitsch to become so ugly that kitsch becomes its own antithesis. Fetishism is here as well -male feet and male noses,  Barbarian-style clothes to cover the scantily-clad lads pirouetting around, phallic secret weapons coming out of crotches or nipple areas etc.The bizarreness of imagery between levels leave you even more confused, even more so when you don't happen to know any Japanese,and can't explain the presence of a male-female pair, two kid angels, and two ripped bodybuilders simultaneously appearing on the screen. The downright-ugly 16-bit music abounds in different genres and styles and is aided by voice samples from many sources, making bizarre audio collages make the visual aspect even more bizarre.
I guess your background, upbringing and cultural values, taboos and tastes play a role in appreciating or hating the game, but at least it challenges the notion of what a computer games is and what it should address.