I've seen someone else mention these, but I have to recommend them as well:
Maniac Mansion (1987). It's the first SCUMM (Script Creation Utility for Maniac Mansion) engine game that all its successors use (Indy 3 & 4, Monkey Island, Sam and Max Hit The Road, etc). Really hard game play from what I can remember, and it has a sequel too, Day of the Tentacle (1993), which is absolutely hilarious.
Laser Squad (1988) was among my favourites growing up, they are the precursor to UFO/XCOM (the original from 1993).
Elite (1984), a technological marvel for its time. It's still playable today, and if you liked any of the other space exploration / trader / miner games (E:D, Star Citizen, X4, Freelancer, etc) you will love this.
King's Bounty (1990). I could have sworn this was from earlier. No matter. It's the precursor to Heroes of Might and Magic. Has less balancing than its successors and can get really whacky.
Spy vs Spy (1984). Really fun split screen couch pvp. You set traps in a house with doors everywhere in various places that you hope your opponent will forget about while also hunting the other one and beating each other in a brawl. It can get hilariously complex. But needs another player as there's no AI from what I can recall.
Creatures (1990). It's a platformer where you control a cute bear trying to rescue other cute bears from evil potatoes and mushrooms and birds. And that's where the cuteness ends. Every platformer level finishes in a so called torture level where the cute beat to be rescued undergoes some crazy mutilation by chainsaw, sharks, acid. Has a sequel, Creatures II (1992) and a spin-off (kinda), Mayhem in Monsterland (1993).
Summer Camp (1990). Another platformer, story driven with fun mini games. Has a sequel, Winter Camp (1992).
What alarming things?