Would that depend on what your doctype is? If we're still supporting xhtml 1.0 transitional then <b> and <i> are fully compliant
Well from what I can tell it's still just debate between Web designers. I do not find on W3C (yet any ways) where it says or even implies that it is or will be deprecated.
So far I only find people claiming what is better and why they think so. If anyone has a link to an authoritative site it would be appreciated if you could post that link here.
Rendering of font style elements depends on the user agent. The following is an informative description only.
TT: Renders as teletype or monospaced text. I: Renders as italic text style. B: Renders as bold text style. BIG: Renders text in a "large" font. SMALL: Renders text in a "small" font. STRIKE and S: Deprecated. Render strike-through style text. U: Deprecated. Renders underlined text.
The following sentence shows several types of text:
<P><b>bold</b>, <i>italic</i>, <b><i>bold italic</i></b>, <tt>teletype text</tt>, and <big>big</big> and <small>small</small> text.
This list here from W3Schools also does not show either as deprecated
