The vast majority of board games available today are fun board games for adults. They may be fun for other age groups as well, but they fit in the adult category because adults have already lived through those younger years. It’s what qualifies them to be adults.
That said, it should be obvious that not all board games are fun for every adult. Fun board games for adults I’m associated with might not be the same fun board games for adults you have contact with. Among the dozens that I’ve played as an adult, there have been a small fraction that I haven’t particularly enjoyed. They are few and far between though.
When speaking of adult board games, I’m not going to devote time to those that have risque content. The adult-ness referred to here will only be a reference to an age group, not to games that are for “adults only” because they would be rated R if they were movies.
There are some traditional gateway games mentioned fairly often by those who make suggestions for board games for adults – and I think understandably so. Ticket to Ride and sometimes Carcassonne are most frequently brought up, and I agree that they should be as I would also recommend them, especially for adults who have not yet played anything remotely like a Euro board game before. Yes, that’s how these fun board games have earned the moniker of gateway games. Once people see how much fun these are, they tend to look for more fun board games that they haven’t played before.