After a little investigation it seems that Google is actually showing slightly different page titles in search results (SERPs) from the exact content of the
<title> tag on the specific page.
There are a few different situations. The health page comes up towards the top for me, and it has this title in SERPs:
Health News - Medical, Mental and Dental Treatment ... - CNN.com
The actual title on the page is:
Health News - Medical, Mental and Dental Treatment - Beauty, Nutrition and Fitness - CNN.com
So it seems Google is shortening the title to fit into its 65 or so characters. But instead of simply truncating it, it cuts out the middle so it can show "CNN" which was relevant to the search query.
Similarly for the cricket article, searching for "Kenyans one dance away from semifinals" shows this in SERPs:
Kenyans one dance away from semifinals - Sports - CNN.com
However, if you add "cricket" to the search term, it shows the actual page title (truncated):
SI.com - 2003 Cricket World Cup - Kenyans one dance away from ...
The weather page shows this title in SERPs:
Weather Forecasts, Doppler Radar Reports and Weather ... - CNN.com
It uses a complex chain of redirects, including a meta refresh, 302 and 301 redirect to get to
http://weather.edition.cnn.com/weather/intl/forecast.jsp, which finally displays some content. (Note, this is terrible SEO and the page likely only ranks because it has thousands of links pointing to it.)
None of the stages along the way have the title from SERPs, and the final page has "Atlanta, GA" in the title. This is meant to be localized content (although I'm not in America). So in this case, either the page returns the above "Weather Forecasts..." title for search engine spiders, or Google is seeing that
weather.cnn.com doesn't have a meaningful title and making one up from links pointing to the site.
TL;DR: If a page title is longer than 65 characters, Google may show a different part of the title, depending on the search query. Or if there is no title, it will decide on an appropriate title from links or other sources. As is always the case, this is algorithmic on Google's part and you would not be able to specify this yourself.