Not so many games really. Actually, my favorite thing this year wasn't games but audio recording. My best friend and I would get together in breaks from our different colleges and go on road trips. Our favorite thing was to record ourselves doing skits or other nonsense on cassette tapes while listening to our favorite music. I still have them, some 30 or so. I converted them to CDs in the early 2000s and stored them as files on a now defunct hard drive. However, MK and I would go to arcades still here and there. I watched a lot of movies as well.
Companies Formed
Acclaim, Apogee (became 3D Realms), and Maxis (SimCity) just to name the ones I'm familiar with.
Arcade
I had a single arcade game in a pizza shop in my little college town and it was Sky Shark (also called Flying Shark). It was a vertically scrolling shooter in a World War Whatever setting (WWI plane, WWII targets, and future tanks). I played it regularly outside of Chess with my roommate (who always beat me 'cause I was only mildly interested).

MK and I, on my breaks (he was going to a IT trade school), would hit the arcades, and I remember a lot of 1943: Battle of Midway, played co-op.
What else I saw there might have been: Contra, R-Type, Double Dragon, Dragon Spirit and Xybots. I've played all of these later as ports or in collections.
PC
On my Mac Plus I played Dark Castle sequel, Beyond Dark Castle, and point-and-click game Shadowgate.
Home Console
In a way, I had no home since I was in college and bounced from dorm rooms to my old family home across the year. So I didn't have any consoles. The Atari 2600 was in a box in the attic (possibly sold in a White Elephant Fair already), and I didn't know the NES or SMS even existed. But some foundational titles came out for NES: Castlevania, Metroid and Legend of Zelda (NA release). I've, of course, since played these starting in the 90s, but I've mostly come to love the port of Arkanoid.
Board/Card
Additionally, I wasn't playing board games much, although, I played some older ones (Car Wars, Squad Leader, DnD) with my roommate. I also don't see any releases that are particularly memorable today.
TV/Film
As before mentioned, I watch little TV but most might remember The Tracey Ullman Show (in which the Simpsons first appeared), DuckTales and TMNT (if you were still a kid then), and Star Trek Next Generation (which I could never really get into despite the fact I was a huge Original Series fan). Plenty of video game tie-ins there to play later, for sure.
The films I saw and remember are many. I liked action flicks like Predator, Running Man, RoboCop, Superman IV Living Daylights, Full Metal Jacket and comedies like: Lethal Weapon, Rozanne, Dragnet, Spaceballs, Princess Bride, Planes, Trains and Automobiles and Good Morning Vietnam. A few really disturbed me like Angel Heart and Barfly. And I was into horror flicks, Evil Dead II and Hellraiser, in which I found the costume designs oddly creative and interesting. How I had time for all this, is beyond my understanding today.
Bonus
Comics. I used to read the comic strips as a kid from my dad's Sunday paper back in the 70s, one of my earliest memories. As a teen in the 80s, I read collections from Berke Breathed, Eric Larson, Edward Gorey and the comic strips at the end of Dragon Magazine, especially Wormy by Dave Trampier.

1987 was a big year for comics that I didn't read until later like: Frank Miller's Batman Year One, Alan Moore's Watchman, TMNT, Dragon Ball, and the founding of Dark Horse Comics. Late in the decade, I read The Tick ('88) and Sandman ('89). And I wanted to mention Garbage Pail Kids because collectible cards seem a kind of adjacent art form to comics. The cards came out in '85 and a film was made in '87. They were grotesque, a little like Robert Crumb images. I remember enjoying them around this time.

I loved watching DuckTales when it first came out. After getting tired of Transformers and the other 30 minute commercial cartoons. I kind of stopped watching new cartoons for a while, but DuckTales got me back into it!
As a kid, I could never understand the appeal of Garbage Pail Kids. So many other kids collected them, though.
I have to watch some DuckTales this month. I certainly liked the video games. I'm going to play the first one again on PS3 this month.
In looking through the card art, they are really gross-out images. I guess that's the point but wow, kind of stomach turning.
