The number one problem I have when trying to convince people to play game, or when simply explaining that I play games, is the response that games are a waste of time. Worse, I sometimes hear this from people just after they've played a game that I suggested. "Boy, that was a waste of time."
Undoubtedly, some game experiences are a waste of time. How do you know which ones will be so, before you suffer through them?
There are people who don't enjoy games, and not simply out of ignorance about better games. Intelligent people who already have social, cerebral, or interesting hobbies may simply not be interested in investing additional time to pick up another hobby. And that's fine.
Of course, many people who say that they're not disposed to games hold a mental picture of an activity which has little to do with current gaming. They may picture children's games, play activity, lifelong devotions such as Chess, or strange hobbyists such as miniaturists. It's often difficult to replace these people's prejudices against the gaming hobby, because they wave their hand at you as soon as you try to explain.
Sometimes a really powerful analogy (such as comparing specialized gaming to the wine industry) can help. I like to describe how analog games have evolved over the last thirty years, just as digital games have. Or that fairy tales were once understood to be for adults until the last 100 years or so.
The best solution would be if intelligent games had another name that didn't evoke the associations with those games that these people already have dismissed. For instance: Ludography, Mind Sports, Intelligent Games, Analog Play, or some other name for this hobby might do wonders.
Even people who may be disposed to playing games given the right circumstances, may not be disposed "right now". Timing is important.
While the right game at the right time may give satisfaction of having experienced quality time, when a person is in a foul mood, or has more important things to do, or has issues that need resolving, and so on, they shouldn't be gaming, and especially they shouldn't be forced into gaming. They may also have just played the game three times in a row and need a break from it.
One bad experience due to timing can wreck a game, or the idea of gaming, for a long time. Save gaming for a time when you are open-minded and relaxed, with friends.
A good group of people with which to play games is critical to enjoying the game experience. If you wouldn't have a conversation or a meal with a group of people, you won't want to be playing games with them.
And some otherwise lovely people are just disastrous as game players. While there's a good deal of flexibility as to gaming styles, the essential difficulty is when styles are mismatched. Players who are too serious when everyone else is lighthearted, or vice versa. Players who take a long time to think through moves when everyone else wants to play quickly, and vice versa. And then there are just those who have no game sense, and whose company should be restricted to lesser activities such as talking about politics or Goethe.
Just as there must be a match between players in a group, there must be a match between the game and the group. There are few games that will outright lead to bad experiences; mostly, there are the wrong games for the group.
Some people will feel they are wasting their time when playing games of chance. Others will feel this way when playing complex strategy games, especially against merciless and experienced players. Some balk at a theme, or at an activity, or at an association.
Choose games wisely. As a rule of thumb, if you played the game as a child, you may experience a sense of nostalgia when playing the game, but you'll also likely feel like you're wasting your time; you already learned everything you needed to about the game as a kid. Unless it's a screaming blast to play again and again, why not expand your horizons?
Even the right game with the right people in the right mood can flop, if other external circumstances interfere.
You may not really have enough time to play the game through, or you may be using the table someone's spouse needs to prepare dinner, or you may be playing on a small ledge on a windy mountaintop near a flock of famed cardboard eating goats.
Respect the needs of all players, and remember that games are games. The right games at the right time with the right people can be a meaningful, positive, fun experience. If the wrong elements are at hand, save the games for another time.