The Internet Archive has just posted every edition of OMNI Magazine free for downloading, including beautiful PDFs that capture the art and ads of the time.
Launched in 1978, OMNI had a profound effect on science literacy and people's understanding of tomorrow. From Wikipedia: "Science Digest and Science News already served the high-school market, and Scientific American and New Scientist the professional, while OMNI was arguably the first aimed at "armchair scientists" who were nevertheless well informed about technical issues."
Reflecting the spirit of its times, both the NY Times and The Economist added science sections to their roster a month after the OMNI first dropped. The publication's 1986 cover story on nanotechnology brought that nascent field into the mainstream (see this timeline from MetaModern) and its art helped establish the futuristic aesthetic of the 80s (10 covers here). It was also an early nurturer of nerd culture. As LiveScience notes, "As a short hand for an early version of geek-chic, OMNI appeared in "Ghostbusters", "The Breakfast Club" and "Star Trek IV", and was mentioned in "Jurassic Park" and the remake of "The Fly."
In 1982, OMNI published a "Future Almanac" which, if you were to read it, Ben Bova assured, "very little that happens in the next two decades will be a surprise." By the way, copies of it are available for $4 via Amazon, and yes, I just bought a copy!
Here's an ad for OMNI from 1978 where it declares itself, "The magazine of tomorrow, on sale today."