I guess I would like to be able to include HTML tags within the title so that when the title is listed certain words are bolded.
Is this possible? When I try to put HTML into the title, the tag itself is output (escaped) in the final page list.
Yes, you can use HTML elements in post titles by default. If your output is escaped a plugin or theme might have touched that. Disable all plugins and switch to TwentyEleven. This will help you to identify the source.
Note that markup is stripped in some places where it is not allowed:
Also make sure your markup is valid and allowed for your user role. The