Here are wider contexts for the sentences:
I write emails (Present Simple):
As part of my job, I write emails on a regular basis to communicate with colleagues and clients.
I’m writing an email (Present Continuous):
Right now, I am sitting at my computer and composing an email to send my boss the details of an upcoming project.
I’ve written an email (Present Perfect):
Earlier today, I wrote a lengthy email to the project team outlining my suggestions for the meeting agenda. I've already sent the email, so now I will wait for their responses.