The World This Week and International Times were great programmes, and were often part of my weekend viewing around that time. International Times would air at 7:30am, after Comic Book but before Trans World Sport. Sadly, it only lasted about 6 months. The World This Week was a 7pm programme, if memory serves, and basically acted as part Saturday edition of Channel 4 News, part current affairs programme. Not seen the title sequence for that show pop up anywhere yet. And I was a big Channel 4 Daily fan, prefered it to Breakfast News and TV-am.
Among my favourites that haven't been mentioned so far, the original ITN World News theme from 1987.
Also, the ITN World News 1994 version.
CNN International World News, 1992 version
CNN Headline News, 1994 version
Westcountry Live, original version, which lasted for multiple title sequences until about 1998.