For 52 card, I’m a sucker for trick-taking. So games like Hearts and Spades. One of my friends has been importing a ton of small box games from Japan and Korea, and there are some good card games in the batch like Hachi Train and Nana (aka Trio).
Make sure to check out Schnapsen if you haven't already. Great choice when you only have 2 players. I have a little blurb and links in my other comment.
The classics are good, Crazy 8's, Go Fish (which is better reversed, where you can see other people's hands but not your own), Egyptian Ratscrew, President/Scum, and so on, but I genuinely enjoy Mao the most.
Between the simple quality of the base rules and the fascinating depth, deduction, and memory puzzle as the game progresses... It's wonderful. Sadly, too many people choose to play the game as an inside joke or gatekeeping game, whereas the game is best played with a more teaching role at heart. Still penalize for failure to follow rules, but enunciate why and be deliberate about it, so they have a chance to learn from their mistakes, or others'!
I've been getting into Doppelkopf! It's a trick-taking game with tons of rules and variations on those rules and a kinda weird ordering for the trump cards, but it's quite fun. My favorite thing opposed to other trick-taking games is that you start each round but don't necessarily know who of the other 3 players is on your team. So each round can end up requiring a different strategy!
It's pretty complex, but my gf's mom has been teaching the two of us and her sister, so it's a bit less overwhelming. Tons of people in my department play at university, so I'll finally be able to drop in and play a few rounds with them as study breaks :D
Schnapsen (pagat, WP) - a 2p trick-taking game playable with a standard or German suite deck. A unique aspect of it is that the trick-taking rules change mid-round. In the first half you can don't have to follow suit at all, you can play whatever you want. When the draw-deck runs out or when one of the players decides to "close" the deck the rules change and you must follow suit or play trumps. The timing decision of when to "close the deck" is a really cool one and it's what makes the game.
Regicide - is a co-op (or solo) that does a really good job at giving a varied game experience with a standard deck.
Haggis - a ladder-climbing game that's playalbe with a standard deck with 2 players. Needs custom deck for 3.
Other:
Mottainai - An amazing amount of game in a 54 card deck. Probably my overall favorite card game
Sea Salt & Paper - Very addictive, especially on BGA. It sort of a set collection game with rummy-style hand management that includes some cool abilities you get when you get the right pair of cards.
Love deckbuilders in general. Overall favorite is probably Ascension but also love Star Realms, Clank, Dominion etc. Happy to play pretty much any deckbuilder anytime.
For Northwood - a solo tricktaker. How does that even work? Very well as it turns out! Excellent art and production too.
SCOUT - another climbing game that works well at 2p
Honorary mention to Hats which is this week's favorite. Has some of that Arboretum meanness but plays very differently. It has a card flow that took a while to get used to but very neat once we figured it out.
I play a lot of the classic games on Cardgames.io. Spades in particular is a favorite, albeit I also really enjoy an Icelandic game called "Manni".
My family played a lot of what I later learned to be a variation of Shanghai rum, a contract rummy played with three 52 card decks. It takes a while to get over a full game, but it was always a good time.