As someone who was a computer repair tech for 15 years and has now been a professional programmer for 6 years (with +25 years non-professional programming) (also having done some research on keyboards over the years for gamers as well), there are two words that normally come up.
Click: for the normal, modern era keyboards that are the membrane (quiet) keyboards that most everyone uses in an office or at home.
Clack: for the "old school" 1980's style keyboards that were mechanical keys. These keyboards tended to be really heavy. This word also describes what you might hear at a gaming convention, as many gamers like the feel of mechanical keys over membrane keys. There are even a variety of different mechanical keys you can get for a gaming keyboard, as each one has a different amount of feedback/pressure and sound. I've heard gamers talk to each other about what type of keys they use, including what they feel and sound like.
Both of these words can be strung together with hyphens to note steady typing: click-click-click (for softer sounds) or clack-clack-clack (for louder sounds).
"Clack" can also be used to describe someone who is "energetic" with their typing, even on an office keyboard. They might be typing really fast or really hard on even an office keyboard. "Working in my cube, I sometimes listen to the quiet click-click of nearby co-workers going on about their day. Usually, though, I can also hear Bob clacking away at his desk as if he was in a hurry."
You can also mix them up while stringing them together to mix soft and strong keystrokes. "Joe always had a tendency to emphasize his "Enter" keystrokes, with a click-click-clack of his keyboard."
I've seen "clickety-clack" used in some books, but I don't think I've ever heard it used verbally.
You might also be able to use "snick":
Google noun definition #2
a sharp click.
"he heard the snick of the latch"
"Snick" might be more for a sharp staccato of a single key press, or where a certain key makes a louder sound than normal. "The office was usually so quiet that I could hear Sue in the next cube typing. Her keyboard was weird in that I could hear one key snicking louder than the others."
As B.Fox mentioned, "tapping" could be used. However, that's more of a style of typing (like "pecking") and doesn't really describe a noise, but it would imply a softer sound coming from a keyboard, although not necessarily an actually key press. "Ann sometimes gently tapped her fingers on the keyboard when she wasn't sure what to type. Only occasionally a letter would accidentally pop up on her screen."
As an example of someone who is excessively loud on their keyboard, you can use "banging". "Jeff was banging out his manuscript as if his life depended on it, disrupting the quiet of the office." This can also be used when something bad happens. "Pam banged on her keyboard as the computer blue-screened, again."