Oh heavens yes! Lost films are actually an extremely common phenomenon and professional archivist groups such as NFPS and the Library of Congress Film Preservation Board work actively to slow the loss.

Now as to the question of whether any "important" films have been lost, that's a bit subjective, though the Library of Congress estimates about 75% of silent films have been lost, which is a simply incalulable loss for those wishing to study the history of film.

If you're looking for specific examples of notable lost films, probably the most famous example is [Metropolis](https://en.wikipedia.org/wiki/Metropolis_(1927_film)#Restorations), though restoration attempts have been largely succesful, so that doesn't quite meet the "forever" criterion. [Cleopatra](https://en.wikipedia.org/wiki/Cleopatra_(1917_film)) might be a better example, because it was quite significant in the history of film making, and essentially none of it survives today. On a personal note, if there was one lost film I could find, it would be Humor Risk, the Marx Brother's first film, now totally lost, probably forever.

Poor management? How about a huge chunk of the popular TV series "Doctor Who"? Back in the 1960s, the video tape that British TV episodes were shot on was incredibly expensive, and the cost of storage was very high. Further, because of the expensive rights, many shows didn't seem to have much hope for future reruns. So, a decision was made to wipe the master tapes of "Doctor Who" and reuse them for other productions. This junking continued up until the early 1970s, when fans realized the horror of what was actually occurring. A huge number of episodes were wiped, but a good number of them were recovered because fans realized that a few copies still resided in the UK, and more existed throughout the worldwide British Commonwealth due to overseas transmission. Nevertheless, 97 individual half hour episodes of the program remain completely missing. (As an interesting side story, the audio tracks of every one of those episodes survive thanks to an incredibly zealous early fan who, in the days before VCRs, hooked up a reel-to-reel audio recorder directly to his TV!) This happened with a number of other British TV shows in the 1960s as well. Most notable is the missing first season of "The Avengers", and three extant episodes of the popular show "Dad's Army", but Doctor Who is by FAR the most famous example due to its continuing worldwide success.

Not sure if this is completely relevant here, but the original moon landing videos from Apollo 11 are lost. The original tapes holding recordings from the lunar module in SSTV format were all reused for later missions, and the only videos we have left are those of the TV broadcasts, converted from SSTV.

Many popular South Korean films were lost due to poor storage and management, and recycling of film for other uses. For instance The Housemaid was a blockbuster that was thought lost for many years, but two reels were found in storage, with subtitles scrawled on them.

After owners of factories that manufactured a kind of straw hat popular among farmers realized that a strip of celluloid lent the headgear’s otherwise flimsy brim an extraordinary sturdiness and, at the same time, made for a stylish decorative border, they began to purchase apparently worthless, worn- out 16 mm and 35 mm prints in bulk, once the films had finished their dollar- theater runs. Many classic titles were chopped into thousands of pieces as they were moved on a conveyor belt from exhaustion to extinction. When the popularity of the straw hats dwindled in the 1970s because of a rapid decline in the farming population, innovative chemists developed a way to efficiently extract silver from celluloid film. More invaluable works evaporated in that alchemical process, causing irreversible damage to South Korean film history; over 70 percent of films made before 1960 are now reported missing.

https://www.criterion.com/current/posts/2993-the-housemaid-crossing-borders

There's an interesting possibility that many of them are preserved in Kim Jong-il's film archive; he had a longtime program to copy popular films and ship them to Pyongyang.

London After Midnight with Lon Chaney might be the most famous lost movie. Here's a list of famous lost films from Mental Floss and a more extensive list at Shadowlocked. Wikipedia maintains what is probably the most complete list. For more in-depth details, you might read Lost Films: Important Movies That Disappeared by Frank T. Thompson.

You might also be interested to know that some films once considered lost were rediscovered because when they were submitted for copyright, the filmmaker was required to print each frame of the film on paper and submit it to the Library of Congress. The paper prints have been scanned and the film reconstructed and the quality is remarkably pristine. Some of these films can be found on the excellent Treasures of the American Film Archives collection.

Much of Super Bowl I was lost due to the tapes being taped over. It's been mostly reconstructed now I believe but some parts are still missing.