Privacy note: If your Tweets are public (i.e., not protected), they will still be visible on your public profile page to anyone, regardless of whether they have a Twitter account or not.
We do not send notification to a user when you block them, but because they will no longer be able to follow you, they may notice that they've been blocked.
In addition to blocking users, you can also unfollow users or report accounts as spam. Please read those help pages for more information on unfollowing and reporting spam.
Our Troubleshooting articles for following issues have answers to common problems.