If you'd want to commit a cardinal sin you could try something like:

perl -0777 -ne 'print "$1\n" while(/<b>((.|\n|\r|)*?)<\/b>/gm);' test.
+html
[download]

• the -0777 will slurp the file at once
• the (.|\n|\r|)*?)will match any character including line-ending characters, and match them non-greedy.
• the //gm regex modifiers will match multiple lines and match as much times as possible.

But for more than a quick hack I'd go with the solutions already offered.

Update: to address seattlejohn's <b name=value> problem you could use:

perl -0777 -ne 'print "$1\n" while(/<b\b.*?>((.|\n|\r|)*?)<\/b>/gm);' 
+test.html
[download]

I think there will be lots of other situations where this oneliner won't match, and thats exactly the point why you should use a descent parser.