In Peanuts, there was a series of strips where Charlie Brown goes to summer camp and tries to befriend a kid in the bunk next to him. The kid is always shown with his face turned toward the wall, and never says anything other than, "Shut up and leave me alone!"
Adults are never shown on Peanuts. The only exception were some adult bodies, but not faces, that were visible when Lucy was in a golf tournament, and this was back in the strip's early days.
Downwind Jackson in the Smilin Jack comic strip, whose face was always turned away, usually to gawk at women. Creator Zack Mosley established that Downwind was a handsome ladies' man, but decided to leave his face to the readers' imagination.
MAD did a spoof that revealed his secret - he's actually an ugly little man who is chased by women because he happens to have a $100 bill stuck between his front teeth.
Lena the Hyena in Li'l Abner, who was the world's ugliest woman - the area around her face initially had a blank space with the words "Deleted by Editor." Al Capp held a contest for readers to draw Lena's face. Basil Wolverton won. For the curious, here's the pic◊, but be warned, it's pretty gruesome.
Beetle Bailey — Bettle's eyes have never, ever been seen. Even before he was in the army, he had a hat pulled down low to hide them. They probably just look like dots, though. An early strip confirms your theory. Also, Mort Walker allegedly mentioned Beetle's eyes as being "India ink" -colored. Makes sense.
In one MAD parody someone finally sneaks up to Beetle and rips his hat off. His face is much like you would expect, except that it turns out he was hiding a tattoo on his forehead reading GET OUT OF VIETNAM.
In one actual strip, Lt. Fuzz noticed that he never saw Beetle's eyes, so in order to get a look at them, Sarge snuck behind him and yelled "BOO!" making it fly off his head. Unfortunately, Beetle was wearing sunglasses.
The face of Mr. Pembroke, the boss of Roger Fox in FoxTrot, is never seen. Portraits of himself in his office likewise have the face cropped out.
The title character of The Phantom is a very strange example; he wears a mask in his heroic identity, as most superheroes do (in fact, he was likely the one who started the trend), but even in his civilian identity of Kitt Walker, he wears a fedora, sunglasses, and a trench coat with the collars turned up. The readers have never been able to see his unmasked face clearly.
For the longest time, both Don and Marcie from Safe Havens were never shown above the neck to emphasize their height. Eventually, though, their faces were shown, Don's when his son was born, and Marcie when Rosalind finally meets her (After a series of experiments left her at six foot three).
Phoebe and Her Unicorn: The unicorn Lord Splendid Humility, whose unmatched modesty requires that he never allows anyone to see him. His horn protrudes from his hiding place.