How long should I wait before sending a follow-up email?
The timing of sending a follow-up email depends on context. It is hard to imagine a situation where a follow-up email would be appropriate within a week. If your original email was a “cold call” marketing email, then you can wait a couple of weeks even.
If you are following up on a job interview, then it will also depend on what you were told at the interview. If it was said that a decision would take a week or two, then a follow-up before that might seem pushy.
On the other hand, a delay of three weeks or more runs the risk of being interpreted as a lack of interest. Use your judgment to gauge the appropriate time span.