Chrononauts

Chrononauts, created by Looney Labs (creators of Fluxx), is a card game about Time Travel.

You play as one of several folks from alternate timelines that have suddenly found that history as they know it is gone. Completely. Instead, they get thrown into a timeline completely different than the one they knew - namely, the one we actually saw in Real Life. So, you're a time traveler with the ability to alter time, bounce about as needed, and even fix Temporal Paradox. So, what do you want to do?

Chrononauts is a bit different in that there are three ways to win. You can have your character (you're given a unique character ID, hidden from all others at the start of the game) recreate their own timeline, at which point they go home. You can also have your character become an expert at preventing paradoxes, thereby being hired by the game's Time Police (symbolized by hand size). Finally, you can use your time machine to acquire stuff for some fabulously wealthy individual, and retire to whatever era is pleasant enough for you.

That said, there's also a Rocks Fall, Everyone Dies scenario - if there are at least thirteen unpatched paradoxes at the same time, the entire universe collapses. Good luck with all that.

There's also Early American Chrononauts that focuses purely on early US history; the two games can be combined to make what the developers call Uber Chrononauts. They also released a small expansion set called The Gore Years that focuses on more recent events, and can be added on to the base game or the uber version, and another one called Lost Identities which adds more ID cards.

This game has examples of:
 * Alternate History: Every identity comes from one; one way to win is to get back to your own.
 * America Wins the War: See the conditions under Godwin's Law of Time Travel.
 * Apocalypse How: Planetary Mass Extinction (including humanity) in the alternate 1962; Omniversal Physical Annihilation if too many paradoxes go unpatched.
 * Author Appeal: Some of the ways the timeline shifts.
 * Two of the most notable: handguns becoming illegal in 1999 and marijuana becoming legal in 1986.
 * The "Purple Submarine" Beatles Reunion CD can only be played if John Lennon survives, but it can be used as a substitute for any artifact with regards of your mission.
 * A bit of Player Appeal is mentioned on the Loony Labs website, with certain players going out of their way to kill Ronald Reagan or save John Lennon, even if they have nothing to gain from it.
 * Butterfly of Doom: Most of the linchpins have direct effects within a few years. The one that has the longest delay is saving Abraham Lincoln from assassination. Lincoln abolishes the Jim Crow laws if he lives, which kicks off the black civil rights movement en masse a century early, which eventually leads to Martin Luther King Jr. (if he's also saved from assassination) becoming Richard Nixon's Vice President 100 years later, and then the first black president of the US after Nixon is impeached.
 * Delicious Distraction: The German Cake artifact card, when in play, can be used just like a Memo From Your Future Self in order to cancel another player's action. It's just that good, apparently.
 * Discontinuity: Used In Universe by a card of the same name - all players switch hands (though not identities, missions, or played items) with each other. Beyond simply the effects of potentially getting other players' patches or the like, you also effectively make it that you, and not someone else, patched the timeline so many times.
 * Edutainment Game: The game is apparently very popular among history teachers for "sneaking in learning", especially the Early American Chrononauts spinoff, which covers a very specific timeframe.
 * The End of the World As We Know It: The patch for 1962 is World War III: the Cuban Missile Crisis escalates into global war, and humanity is wiped out. This creates what the game calls Uberparadox - no events afterwards can be affected as long as it's active (though it and all potential issues after it count as a single paradox for the "all lose" scenario). Only two characters look to have this patch active - a hyper-evolved cockroach and a Space Alien exploring the past of the destroyed Earth.
 * Liberal Counterpart: 'Senator Lennon' apparently becomes this for/to Ronald Reagan, if he survives.
 * For Want of a Nail
 * Godwin's Law of Time Travel: If you prevent Pearl Harbor and Hitler wins, this trope comes into effect.
 * Gone Horribly Wrong: Ginohn's backstory.
 * Historical In-Joke: Several.
 * Hitler's Time Travel Exemption Act: Extremely averted - Hitler is extremely vulnerable during the 1936 Olympics, and it triggers five different potential paradoxes. If two different players are both trying to win via the "return to your timeline" goal and they each involve different quantum states of Hitler's existence, expect to see Hitler assassinated and saved from assassination repeatedly.
 * It Will Never Catch On: You can actually ensure whether or not zeppelins do catch on.
 * Just for Pun: Most of the dinosaur's names are puns.
 * The triceratops is named "Sarah".
 * The tyrannosaurus is named "Rex".
 * The brontosaurus is named "Emily".
 * The stegosaurus is named "Steggy".
 * Multiple Endings: Interestingly, every victory condition has a different justification, and as such what happens to you depends on how you win;
 * Getting ten cards by playing patches means you get hired by the Time Police for all your work.
 * Completing your mission by getting artifacts means an eccentric billionaire or somesuch pays you a lot of money and you can retire to a timeline of your choosing
 * Getting the timeline to match your own means you can return home and finish your life.
 * This also applies to the four different patches that can be used to fix a paradoxed 1945 (the end of World War II): either the Allied forces invade Japan, Tokyo is nuked, world peace is achieved or the Nazis win.
 * No Celebrities Were Harmed: Averted, except with Jesus. The Crown of Thorns card simply states "Worn by You Know Who".
 * No Ontological Inertia: Played with - for the most part, you constantly continue to exist, as do all items you currently have. However, it is possible for items to be destroyed by making them never exist to begin with, and you can even have your identity destroyed by anyone playing the "Your Parents Never Met" card. That said, you continue to exist - but you get a new identity.
 * Prequel: Early American Chrononauts, which can be combined with the main game to make what the developers call "Uber Chrononauts".
 * Reed Richards Is Useless: Averted; among the future artifacts you can acquire are a cure for cancer, a matter duplicator, and Infinite brand super-batteries.
 * Ret-Gone: The "It Never Existed" card... does Exactly What It Says On the Tin.
 * Retroactive Preparation: The "Memo from Future Self" card effectively works like this, instantly negating the last card another player played. The German Chocolate Cake artifact can also be used as a Memo and the image on the card shows it having a postcard attached. Though, Word of God says that it is not the postcard but the cake itself, and that the cake is just so good that it distracts the other player from doing what they just did.
 * Rocks Fall, Everyone Dies: If 13 paradoxes are active, then everyone dies and loses (unless you have Crazy Joe from the expansion pack, who wins in this scenario). In Uber Chrononauts, this kicks in if a given block of four rows has 13 paradoxes.
 * Rubber Band History: You can always, with enough appropriate cards to revert events, recreate the starting timeline.
 * Shout-Out: To several other time travel stories, including Back to The Future ("Grey's Sports Almanac") and, of course, H. G. Wells' "The Time Machine." Most are found on the identities (like Crazy Joe's post-time line restaurant). The creator keeps a (somewhat incomplete) list here.
 * There's now a licensed Back to The Future version of the game, with different rules for changing time linchpins and a new rule for winning: you change the timeline and then stop Doc Brown from inventing time travel in the first place, thereby locking the timeline into YOUR version.
 * Solitaire: A single-player game variant involves getting a number of time travelers back to their home times with one pass through the deck.
 * Temporal Mutability: You can change history as much as you like provided you keep an eye on the number of unresolved paradoxes.
 * Temporal Paradox: The paradox rules are thus. The timeline can only be directly affected at certain points, called linchpins. If a linchpin is affected without the appropriate temporal patch on hand, it creates a paradox. If you do have the proper patch, though, the paradox is resolved. And never let 13 paradoxes exist at the same time.
 * Thirteen Is Unlucky: See Time Crash below.
 * Time Crash: If there are ever 13 unresolved paradoxes on the timeline, then the universe implodes in a Puff of Logic and everyone loses. (Unless you're Crazy Joe from the Lost Identities expansion, who comes from a post-Time Crash future. In that case, you win.)
 * Timeline-Altering MacGuffin: Grey's Sport's Almanac, in a Shout-Out to the former Trope Namer and possible ur-example.
 * Time Police: Though they don't have a lot of direct effects on the game, they do justify several tropes.
 * Timey-Wimey Ball: Mostly averted; time travel works on fairly defined terms. That said, it isn't quite clear why patches are destroyed if the timeline flips twice, and the arbitrary number of paradoxes that cause universal destruction isn't quite explained either.
 * Variable Player Goals: as noted in the description, every player has a unique ID and Mission, and the generic hand size goal. There's also one ID (Crazy Joe) that makes the "all lose" scenario "you win" instead.
 * Write Back to The Future: The card "Memo From Your Future Self," which counters any card potentially used. It can even counter a "Memo" used by another player.
 * Xanatos Gambit: With multiple ways to win, you could be in a situation where if, for example, someone sets back your character's goal, it could allow you to play more patches, increasing your chance to win by having a hand of ten.
 * Gambit Pileup: Except that patch might be just the one someone else needs to get home, but then someone else renders the whole thing moot by killing Hitler again because they want to play the German cake...
 * Xanatos Speed Chess: Inevitable in a game with multiple players trying to reach one of several possible goals.
 * Zeppelins From Another World: If you prevent the Hindenburg disaster, you can cause a timeline with these.