This following pages describe the creation/editing forms for each of the commonly available block types. Some sites may have additional block types specific to them.
All block types have a required Title field, so you will have to give every block some kind of a title. However, if needed, you can uncheck the Display title checkbox to hide the title from the public. Note: unchecking this box hides the title completely, even from screen readers.
The rule of thumb is that if a block is the start of a new concept on the page, then it should always have a proper (and displayed) title that succinctly describes what follows. However, there is a common and acceptable place to hide the block title: when the block is the first one on the page and is simply providing an introduction to the rest of the page. The easiest method for setting up these blocks is to just type "Introduction" into the title field and then uncheck the Display title checkbox.