You've made a great game, but can you do something to the game, to have it be playable almost endlessly?
The answer to this question lies in how different each game will be. Some games have relatively simple concepts, that create fairly deep strategy (Chess, for example.) Others are just wildly different each time, because there are so many possibilities. The tile-laying game Carcassonne, for instance.
Others get a bit samey. For those games, you'll want to add a mechanic that makes each game different. Not so different that it doesn't feel like the same game. Just different enough that the player has to rethink their strategy.
The best way to do this is usually to vary the setup of the game, while leaving the objective and rules of the game the same.
Agricola's "family version" is one example. It's a great game, but after a few plays, I'm doing basically the same stuff — growing crops and/or breeding animals. And here's where Agricola shines: In the full version of the game, each player begins the game with a hand of cards that affect how the game works. For instance, the Berry Picker gives me a free Food whenever I take Wood. Even a few simple cards like this warp the game enough that I need to rethink my strategy every game.
Remember that some games have sufficient innate variability. Typically, games with spatial elements have huge potential for variability.
This is a common mechanic, where each player has a unique rule, bonus, or objective for the game. "This time, you're the Romans", or "This time, you're the Doctor." These add replayability, but only as much replayability as there are different powers. A game with six different player powers just lets players play six different ways, and no more.
The key to adding replayability is to have multiple factors that vary. Consider "this game you're the doctor, and your super-power is... invisibility!" Each of the variable factors makes a small change to the game, but there are many combinations of factors, that will interact in countless ways.
In Santorini, players move around a 5x5 grid, building towers, piece by piece. The objective is to climb to the top of a tower. To add replayability, there's a deck of dozens of Greek gods. Each player is dealt one at the start of the game, and these cards make a significant change to how the player plays the game. These are interesting and impactful variable player powers, that affect movement, building, interaction with the opponent, and much more. Because each player has a god card, and they interact with each other through the gameplay, the game actually does have multiple variable factors. The god Pan is the same every game, but his strategy against Ares is vastly different than if he's against Demeter. This interaction creates endless replayability.
I know Dominion's cards like the back of my hand, but I still play it. Each game, there are ten different types of cards for sale. This would get boring after a few games, except that the ten types of cards are selected from amongst dozens. Even if only one card were different, the strategy for that game would likely be completely changed.
Despite having multiple variable factors, these should all be limited to one part of the game. For instance, a player could have two different character cards each game, but not one variable card, and a variable board. People want to play the same game again, not have a totally different and unfamiliar experience.
Extra variability should only be added when a game is clearly lacking replayability. Some designers seem to just throw variable setups and powers into every game they make. Only add variability if the game needs it.
If you provide multiple different paths to victory, the player shouldn't just choose one arbitrarily each game. Some games have many paths, but there's no reason for a player to choose a different one, other than the fact that they haven't tried it before.
If your game has some kind of mini-objective, or some other thing that isn't a player power, give each player one or two to begin the game with, to give them a nudge in a new direction.
If your game doesn't have a setup that's variable enough, people will quickly work out the optimal early moves. They'll discuss them, and anyone who reads it won't want to play your game any more.
The game Tzolk'in has only a slight variation in starting resources, and nothing else. Now, almost all players start with one specific series of opening moves.
As much as I'm in favour of replayability, it's not as important as the actual gameplay. Making your game worse, to allow it to be played more times, is self-defeating. Some games are correct to have limited replayability. I'd rather have an 8/10 game that's playable ten times, than a 7/10 game that's playable a hundred times. I can just play the game ten times, and then play something else.