I use it. I didn't find it easy to get the hang of it at first. I only follow a few people permanently. I think it is unlikely that anyone will get a message from some of the more popular Tweeters (although I knew somebody who got one from Stephen Fry.) It is also possible to send personal messages which cannot be seen by anyone else. Some people send Tweets which I cannot understand because I am not familiar with their group or their jargon or slang. Others are great Tweeters. Can be very useful for keeping up to date with a person or organization.
I don't have an account but I used their search feature for the student protest updates... and I like seeing what the (fictional) Queen tweets and the Archers' characters' "Twitters" are a laugh as well
Me and a couple of friends follow each other, but we don't log into Twitter regularly, so it's a waste of time really. Much easier to speak on the phone or text. So it is mainly for following famous people and celebrities of various kinds. It's a self-publicity thing more than anything else.
When you block a person, they can no longer invite you to a private message or post to your profile wall. Replies and comments they make will be collapsed/hidden by default. Finally, you'll never receive email notifications about content they create or likes they designate for your content.
Note: if you proceed, you will no longer be following .