Long before the Marvel Universe had stories where its superheroes turned into the undead as Marvel Zombies, Marvel Comics actually had a trademark for the term "zombie" itself. At the time, mainstream and pop culture was just starting to embrace more tales about the dead coming back to life, and Marvel wanted to cash in. However, they did run into some problems, which led to the loss of the trademark, though leaving behind an incredibly interesting story as to how it all played out.
Back in 1973, Marvel Comics and its parent company, Magazine Management, created Tales of the Zombie. They brought in a variety of writers for the 10-issue series including Steve Gerber (known for creating Man-Thing and Howard the Duck) as well as Uncanny X-Men's Chris Claremont. While the strict Comics Code Authority had very concrete rules banning depictions of vampires, werewolves, and zombies in comics, Marvel and Magazine Management got away with Tales of the Zombie by structuring and selling it as a magazine, rather than classifying it as a comic. As such, there were less regulations, allowing for more graphic imagery and more colorful language for a much more adult audience and demographic. They also took the zombie character Simon Garth to serve as the magazine's main character, taken from a Stan Lee and Bill Everett horror story that was published before the existence of the now defunct Comics Code Authority. Brother Voodoo was a featured character as well.
Wanting to capitalize on the series' success, Marvel decided to file a trademark on the term "zombie" itself in 1973, hoping to create more stories about the undead in the future and become the only place for readers to find stories about this particular type of the living dead. However, by the time the trademark was approved in 1975, the series had run its course after 10 issues.
Without the presence of an ongoing zombie series, Marvel lost the trademark in 1996, when a request to have it cancelled was approved. The term "zombie" was just too general of a term, and Marvel's approval for the trademark in the first place is a bit of a mystery. One can imagine how hard it would've been to enforce.
Funnily enough, Marvel Comics did register once more with the trademark office for the term "Marvel Zombies" back in 2006, though this one did not apply to the term "zombie" in general. This new trademark was the result of the emergence of The Walking Dead's Robert Kirkman, and his story about the heroes of the Marvel Universe becoming infected as super-powered zombies with an insatiable hunger. Kirkman's story would spawn several more books set in their own universe, and writer Phillip Kennedy Johnson is currently mid-way through a reboot tale Marvel Zombies: Resurrection, featuring Spider-Man as one of Earth's last surviving superheroes. As such, Marvel's trademark of the much more specific "Marvel Zombies" has proved to be a much better investment.