As a general rule, I do not want to "ignore" tags, because sometimes I find (or even ask) questions that interest me, even in areas that, for the most part, I do not want to read. However, it would be nice to have a quick way to toggle between "see only questions with interesting tags" and "see all questions [except those with "ignored" tags]." Alternately (if slightly less happily), I might create a list of "ignored" tags if I had a way to toggle whether the "ignored" tags are actually ignored. Is there a way to do either of these?

[Side note: what happens if the same question, having multiple tags, qualifies as both "interesting" and "ignored"?]

In addition the preference CSiegel mentioned, you can also use javascript to hide all questions which don't have "interesting" tags by pasting this into your location bar and hitting enter:

javascript:$(".question-summary:not(.tagged-interesting)").hide();void(0);

If you want to do this often, make a bookmark in your browser with the above code as the "location". When you want to hide "non-interesting" questions, just click the bookmark.