We enjoy the board game Labyrinth. Easy to learn and play. There are ways to up the challenge level as needed. For card games, my son really likes Exploding Kittens and both kids like Sushi Go and Sleeping Queens.
I can agree with everyone on Exploding Kittens. We have recently been playing a lot of Tenzis, Slapzis and Cobra Paw- games about quick/careful hands and less about strategy. But they move quickly and are high energy. For more strategy-based games (that might lean more 10 years old than 7) we love Bananagrams & Code Names. And then our little always raves about Taco Cat Goat Cheese Pizza and One Night Ultimate Werewolf (both games that she has played in other households).
I agree on Exploding Kittens, Sleeping Queens, Ticket To Ride Junior, and Uno! When playing with adults that can offer a little assistance, all of us (2 adults, an 8yo, and a 12yo) love the strategy/deck-building games Dominion, Star Realms, non-junior Ticket to Ride, and Catan (have not yet tried Catan Junior). Code Names is also fun with a mixed-age group. My 8yo loves Boss Monster, Minecraft Card Game, and Pokemon (which requires a separate deck per player; you can buy full playable starter decks). He also learned how to play klondike solitaire and was pretty into that one for a while.
My 7 year old likes Sleeping Queens, Kittens in a Blender, Uno Attack (fun spin on regular Uno), Goblet Gobblers (deceptively difficult - he always wins), Skipbo, Othello, Incan Gold, and Fluxx. There are SO many great games out there now - far better than the ones we grew up with.
You've got some great suggestions. It's like all we've done with our kids is play board games all year (haha!) I will pipe in with ours. Sushi Go, Code Names, Sorry, Clue, Rummicube (great for math skills). Prime Climb (also amazing for math skills). Yahtzee, Boggle, Crainium Jr.
I played with a bunch of kids a game called Spot It. It was easy and fun and has different versions and age groups. I like games that are quick to explain and cross generational so everyone can join the fun.
Telestrations is a good game for kid that age (and is fun for adults, too). My son loves playing it. My son likes Blokus and Scattergories, too. He's turning 10. He really liked playing Rummikub, also. Rubik's Race is a great 2 person game kids that age can easily play.