There is much debate concerning the significance of the Bold <b>, Strong <strong>, Italic <i>, and Underline <u> tags. In general these tags have little to no effect on page ranking and should be used sparingly to highlight words of importance such as terms, titles, or quoted text. Repeatedly marking all keyword with the bold tag has very little effect on ranking. It is much better to use keywords in heading tags.
Excessive use of any of these tags makes the text difficult to read, because the reader has to figure out why the words are important, and if there are many occurrences their visual significance is diminished.
Each one of these tags gives the content greater visual significance. They should only be compounded when necessary.
This is a poor use of compounded style because one of the tags is sufficient. This sentence is better just using bold. It still has the same impact.
In this case we can use a compounded style because Greg said "Sometimes compounded style are good to use." It is useful here because the Italic tag indicates that the text is quoted and the Bold tag stresses the intonation of the quoted text.
Bold <b> or Strong <strong>
Both of these render the text in a similar visual appearance. Using Bold <b> is the traditional method defined in the HTML specification. Strong <strong> is the replacement for Bold <b> and is used in XHTML specification. XHTML Transitional allows the use of both but it is recommended to use Strong <strong> instead of Bold <b>. XHTML Strict does not allow the use of the Bold <b> tag and causes the page to fail validation will normally results with a negative affect on Search Engine Ranking.
Underline tag not in XHTML Strict
It is also important to note that the Underline <u> tag has been deprecated from XHTML Strict and should therefor not be used as it will cause the page to fail validation and negatively influence Search Engine Ranking. An Underline can still be applied using Text Decoration style tag <span style="text-decoration: underline"> but it is better not to use it at all. Most current online editors still use the <u> tag and should not be used.
By default Hyperlinks that use the <a> tag have the text-decoration style applied. Some designers prefer to remove the underline and use color or italics to differentiate links from normal text. If this is the case then you should not apply inline style to make the link underlined. A consistent visual style for links is very important for a reader to quickly identify what can be clicked. Adding inline style overrides on links typically confuses the reader.