The horrifying Halloween-themed strip◊ in 1989 depicted Garfield waking up in an abandoned house to learn he's in an alternate reality where he no longer exists. Unable to cope with being alone, he screams out "I don't want to be alone!", and the next thing he knows he's back in his own time again. Some fans speculated that this meant Garfield was really in an abandoned house and slowly starving to death, and imagining future strips in a never-ending state of denial. Jim Davis himself has said that this is false; he had wanted to write a Halloween strip that was actually scary, and decided on what he felt was what people feared the most: true loneliness.
"An imagination is a powerful tool. It can tint memories of the past, shade perceptions of the present, or paint a future so vivid that it can entice... or terrify, all depending upon how we conduct ourselves today..."
One of the scariest things in this series was the exterior of the house; that panel is a masterpiece of utterly-terrifying desolation. Compared to other haunted houses in all types of media, this would be the one that the Ghostbusters would avoid completely.
There have been at least two strips in the early 80s where Garfield ends up being eaten alive by a dog.
This strip. The way Odie looks like on the last panel...
Not on the strip, but in the Garfield.com game "Scary Scavenger Hunt." One of the levels involves going into a dark attic and interacting with a talking Binky doll who gives you a hint on a puzzle. After you complete the puzzle and try to talk to the doll again, his eyes turn red as he shouts directly at the screen "STOP BOTHERING ME!" Oh, and it'll cost you some hit points, so don't do this.
In Scary Scavenger Hunt 2, there's a picture in the hallway next to the spider musical room it's a picture of Garfield sleeping in his bed the game tells there's a hidden clue in the picture after you stare at it for a long time it suddenly shows a dark red demon pig face with glowing orange eyes, snout pig nose, and crooked teeth with a LOUD SCREAM! It returns back to the Garfield picture saying Gotcha! The Binky Doll was scary enough in the first one but this screamer is worse! But on the bright side, it doesn't cost you hit points. But still avoid it at cost!
The scene in the first movie where Garfield sneaks into the train controller room in order to get the train Odie is on back to the station. He accidentally rewires the tracks so every single train will crash into another one, and the entire time, he's making snarky comments about it. ("Seattle? I don't care about Seattle." "Sheesh, you sound like my mother.") Fortunately, he presses the "Cancel" button seconds before they crash.
Also Odie being shocked repeatedly with the shock collar.