I'm not sure how rare these are, but they're fun:
I believe
Race for the Galaxy was one of the first games to make it a tactical decision which phases of play should take place in each turn. It is indeed a race, rather than a battle; you can't directly attack other players. You can disadvantage them, though.
A silly but fun game of growing and harvesting many weird kinds of beans:
Bohnanza ("Bohn" is German for "bean").
I don't know if this one is still in print:
Illuminati. You play a secret society of some kind which is secretly taking over all the world's innocent organisations and groups. So for example the Gnomes of Zurich can take over the Mafia, then use the Mafia to take over the Boy Scouts, and then use both the Mafia and the Boy Scouts together to take over the International Communist Conspiracy (which is not secret enough to be a player group). It's maybe not really a card game as such, though, so much as a boardgame without a board and little cards as playing pieces.
The same company also makes the
Munchkin card games, which are fairly complicated competitive card games that are also RPG send-ups.
For laughs there are quasi-games like
Exploding Kittens and
We Didn't Playtest This At All. Exploding Kittens is actually a game with real strategy, and it tends to get quite tense at the end, but for me at least all the ridiculousness somewhat overshadows the strategy and I need beer to keep playing. WDPTAA is more of an anti-game, hilarious if you're into games much because of how brutally it violates every good and right principle of game design.
A fun serious one we tried recently:
Coup. It's nice because each game is short and has an ominous momentum: something quite bad happens to somebody every turn and it's obvious from the start that this will not last too long. What's not obvious is who will be the last standing.
A weird game:
Hanabi. It's cooperative, but you never get to see your own cards, but only the cards of the other players, and you can't tell anyone else what they have. Nevertheless you have to decide which of your cards to play each turn. It's quite challenging.
A surprisingly good card game: the
Pop-Tarts Game, made (or at least licensed) by Kellogg's. It's quick and easy but somehow fun and not trivial.
One that's always a go-to game for us with mixed groups of guests:
Dixit. You deal out hands from a deck of truly weird images, and on each turn one player selects one card from their hand and says something—a word, a phrase, just a sound, anything. Then every other player selects a card from their hand, and all the cards are shuffled and laid out face-up. Each player except the one who chose first and spoke makes a secret-ballot guess at which card was that first person's card. The first person gets points if at least one other player guess correctly, but not if all of the other players guess right. The other players get points for guessing the first person's card correctly, and also for getting other people to guess their cards. So to win the first player has to match the card they select and whatever utterance they make, well enough that at least one other player will recognize the association as a clue and pick the right card. They can't just make the clue totally obvious, though, because then everyone will see it and they'll get no points. Meanwhile the other players are all trying to select the cards from their hands which could most plausibly be associated—somehow—with whatever the first person said, so that they can get points by enticing others to vote for their cards. Dixit works well with players of all different ages or with different native languages, because everyone has to try to take into account how the other players are likely to think. When you're the speaking player you're allowed to say something that you think is a private association that your spouse (or someone) will surely recognise and no-one else will; it's not considered cheating because it rarely works as expected.
Somewhat similar in spirit is
Codenames, where a bunch of cards with random words (or in another version, pictures) are laid out on the table. On each of two teams one player knows a subset of the cards to be their team's codenames; in each turn this player has to say one word which their teammates will associate with one or more of those cards, but not with any other cards that aren't in the team's codenames set. You also announce the number of cards to which your clue is supposed to apply. The two teams take turns speaking clue words and pointing to cards, until one team has found all its correct cards. So in each turn you're trying to find the magic word that will simultaneously pick out as many of the right cards as possible while not mistakenly indicating any of the wrong cards. Our family record is six cards with one word. In one case it worked because the clue-giver realised that six of his cards were in some sense a place, while none of the wrong cards could be considered a place, and so he just said, "Place: six." The other time we made six, the associations were all kind of tenuous but the clue-giver and I were just on the same wavelength somehow and I managed to make all six right guesses.
The current winner for us, though, is
The Crew. This one has kept a portion of my family up into the small hours several times. It's a trick-taking, suit-following game with Trump, like Bridge or Whist, but it's cooperative. You can only give the other players very limited information about what cards you hold, but over the course of each hand you have to manage together to accomplish a number of missions, typically involving one particular player taking a trick containing one particular card. You get to use all the great old card-playing tactics like establishing voids and returning leads, only now you're all working together. Some of the later missions are really hard, like getting each person to take their assigned cards while ensuring that no player's trick count ever gets ahead of any other player's by more than one trick. Or ensuring that none of the highest cards ever manages to take a trick, or that all of the lowest cards do take tricks.