When I was watching YouTube reviews on mechanical keyboards before I bought my mechanical keyboards (note the s after keyboard, because I had to buy two), I came across a site one guy used to test how well he could type on the keyboards he reviewed. It was called typeracer.
What you do on that site is, type - as fast as you can. You are given a paragraph to type and it shows the realtime words per minute. You have to type in the correct case, type the punctuations and type with correct spellings (correct, according to the paragraph) to finish each test. To make it fun, they have made it like a game, hence the name typeracer. While there is a practice mode which doesn't record the performance into your profile, this racing mode which you race against other people (or racers) records your performance into your profile. Of course, if you are cheap, you can close the race midway if you feel you are not going to get a good score and it will not be reflected in your profile. By default, you will be racing against some random people who are logged on like you, but you can also race against your friends by inviting them to a race. I haven't used this feature yet, but I think that is the most fun part of it.
So far I have done over 500 races and I average about 70 words per minute. There are people who can type faster than 150 wpm and you can check some videos on YouTube where they do it in real time. It is amazing how fast some people can type. Buy they have few tricks up their sleeves which I don't use. If they misspell a word, they would quickly press Ctrl + A to select all the text you typed into the text box, and type the word from the scratch. I don't do that. I use backspace to erase letter by letter and correct it. Doing the former method would save a lot of time in typeracer, but you cannot do that in real life when you are writing a document. I want to improve my real-world typing speed by improving accuracy, not by employing these typeracer specific "tricks". So I will probably continue to do it the way I do now.