There are only a handful of good ones, and they are built for different things. Here is what each is actually for.
Worth saying up front: this page is on the Keywraith website, and Keywraith is one of the games on it. Everything else here is listed because it is genuinely good, and in several cases it is a better answer than mine. Where that is true, the page says so.
Most people arrive at this question having played ZType and wanting more of it. That is a narrower ask than "a typing game", because ZType is a shooter: enemies come at you and typing is how you fire. A typing test is not a substitute for that, however good it is.
The two browser games built on that idea are ZType itself and Keywraith. If you have not played ZType, play it first. It is the original, it is free, and it is a complete thing in about ten minutes.
Keywraith takes the same core, typing a word to destroy the thing carrying it, and builds out from it: a dodge and an ultimate, enemies that change how a word must be typed (one re-rolls until you commit a letter, one erases your progress on a single wrong key), three difficulty paces, six handcrafted levels ending in a boss, and a daily challenge shared by every player. The full guide explains all of it.
The typing shooter almost everyone means when they ask this question. Words drift down, you type them, they die. Free, browser-based, made by Dominic Szablewski in 2011 and still the reference point for the whole genre.
Pick it if: You want the original. It is short, sharp and needs no explanation. Visit ZType
Not a game. A typing test, and the best-looking one there is: endlessly configurable, open source, with detailed history and graphs of your speed and accuracy.
Pick it if: You want to measure yourself, not play something. The two goals are genuinely different. Visit Monkeytype
Real-time races against other people, typing quotes from books, films and songs. The competition is live and the text is real writing rather than word lists.
Pick it if: You want other humans to beat. It is the most social of these by a distance. Visit TypeRacer
Typing races with cars, garages and progression. Widely used in schools, and built around collecting and levelling things up alongside the typing.
Pick it if: You want progression and reward loops, or you are looking for something for a younger player. Visit Nitro Type
Touch typing lessons that adapt to the letters you personally keep getting wrong, rather than drilling everyone through the same sequence.
Pick it if: You cannot touch type yet. None of the games on this list will teach you the layout; this will. Visit keybr
If you want to play something, ZType or Keywraith. If you want to race people, TypeRacer. If you want to measure your speed, Monkeytype. If you cannot touch type yet, keybr first and then come back.
These are not competing products so much as different answers to different questions, and the fastest way to be disappointed by any of them is to pick one that was built for something you did not want.
For pure arcade play, ZType and Keywraith. For competing against other people, TypeRacer. For measuring your speed, Monkeytype. They are all free and they are all built for different things, so the honest answer depends on which of those you actually want.
Keywraith is the closest in spirit. It keeps the same core idea, typing a word to destroy the thing carrying it, and adds a dodge, an ultimate, enemy types that change how a word has to be typed, a six level campaign and a daily challenge.
They improve typing under pressure, which is a real and slightly different skill from accuracy at rest. None of them will teach you the keyboard layout from scratch, because none tell you which finger to use. Learn the layout with something like keybr first, then these get much more rewarding.
Not really. Every game here needs a physical keyboard. An on-screen keyboard cannot keep up, and most of these are desktop and laptop only by design.