"New Posts" shows posts that you haven't yet read. These can go back quite some time (limited by the forum's max limit).
Today's posts shows unread posts from Today only.
My Posts shows only threads that you have posted in.
There is no way for you to remove items from this as it uses a standard sql query to find posts based on your username. This is a feature that people use all the time and not something that I've ever seen anyone ask to have removed in the years I've run various forums, 2 with 30,000 plus active members.
New Posts shows posts that you haven't yet read.
Technically you are correct that they go back quite some time, but what is important is the top 10 new posts have only just been posted in the last 5 minutes. This is an ACTIVE forum, with potentially millions of smokers who might participate.
Today's posts shows posts from today, not UNREAD posts from today; in a practical sense, it shows almost the same as New Posts.
My posts shows threads you have ever posted in; what you'd want to see is UNREAD POSTs in threads you have posted in.
I currently have 7 pages that show up of threads that I have posted in, but I wouldn't normally notice if there is activity going on in a thread that's on page 7 because I'll never go back that far; I probably just have to figure out how to bump threads up and down that page; I *thought* it shows them in the order that I last posted so I suppose if i wanted to bump a thread up my list I just have to post on the thread; kind of spammy; but its some other order; would be nice to be able to filter some out if i just got tired of a thread, like the clone wars thread; or maybe mark some as higher priority or interest or something.
Sometime you want to follow a thread; sometimes you might want to unfollow a thread.