Four places to play, and what each one is actually for
There is no single best game site. There is a best site for the next half hour. I use four, including this one, and I can say what each is good at without pretending the others do not exist.
Poki
Poki is the large, fast catalogue. If a child says “I want a car game” or “I want a new runner” and does not have a title in mind, this is a reasonable first search. You will find a lot, including games that are only okay. The site is free in the browser. Some features around a game may ask you to sign in. The games themselves are made by many different studios, so the feel changes every click.
CrazyGames
CrazyGames overlaps with Poki and then goes further into multiplayer and slightly heavier browser games. I open it when the thing I want is a live match with someone online. FreeGameToPlay does not run a lobby. Same-screen play is on the 2 player games page, and a finished round can be sent as a challenge link.
Coolmath Games
Coolmath Games is the puzzle site a lot of people already trust from school. It earns that. If your hour is sudoku, logic, and quiet boards, it is a deep shelf. It is not where I look for a runner or a shooter.
FreeGameToPlay
This is the small shelf, and it is the one I can stand behind game by game. No account on any title. Sudoku Master when I want a real puzzle. Dino Flip when I want a dinosaur run. Tic-Tac-Toe when someone is next to me. Bubble Beat when I have a thumb and two minutes. Mech Fury when I want to get better at a fight. Cat Cafe when the person holding the phone is seven. After a round, Challenge a Friend puts that result in a link. They open the game and try to beat it. Still no account.
The full list is short enough to finish. Categories are puzzle, arcade, action, and strategy. If one of those is the hour you have, start here. If you finish the shelf and still want more, go to one of the three above. That is a normal way to use the internet.