The <i> is a valid part of HTML but its purpose is not to indicate emphasis - that's the job of the <em> tag (as used in this sentence). Instead the <i> tag should be used for all of the other instances where there is a convention of using italic text where the intent is not emphasis.
Here's a list of some of the places where it is appropriate to use the <i> tag in English (rules for other languages will almost certainly be different).
There are probably many more specialist fields where italic text has a special meaning but the above list is sufficient to show why the <i> tag is required in HTML.
This article written by Stephen Chapman, Felgall Pty Ltd.