Most likely, your theme uses some form of CSS reset. Your markup (“b”, “i”, etc) is probably being saved and rendered correctly, but the CSS reset overrides all of the styles that the browser would normally apply. Try viewing the source of your page, and see if the markup (“b” tags, “i” tags, etc) actually exists. If so, you’ve got a reset problem. All you need to do is add styles specific to whatever container wraps your posts (probably a div with the class “post”). For example, to make your b tags bold again, you might add “.post b { font-weight:bold; }” to your stylesheet.
The other possibility is that you’re using the_excerpt() to render content. By default, all markup is stripped form excerpts–this is expected behavior. You won’t see any formatting at all unless you use the_content() or something equivalent.