I'm looking for an MPEG clip of George Bush Senior's visit to Japan
some years ago, and more specifically, the scene in which at a state
banquet he was ill over the Japanese Prime Minister.

The event you're referring to happened in 1992 at a state dinner. 
Yahoo! (the original version) wasn't even around at that time, and the
'web' was still in it's infancy.  While I'm not saying it doesn't
exist in some form, I'm sure that news video from that era would be
hard to come by on the web.

This site promises a clip, but it looks as though you need to register to view it:

http://www.newsplayer.com/searchresultsf.asp?featureID=32&page=1

Thanks bowler-ga for a lead to a great site - i paid my subscription
(not much .. only GBP4) but the clip only showed the scenes outside
after the event and not the event itself and I needed the event
itself. Can I leave the question open for a while and see if anyone
can find it?

The Daily Telegraph: "The incident spawned a new verb in Japanese -
"Bushusuru", to throw up or, literally, to "do like Bush". " (Bush
finds plenty of PR in a pretzel , 15/01/2002)
http://www.telegraph.co.uk/news/main.jhtml?xml=/news/2002/01/15/wbush115.xml

I'll search for it in Japanese. stay tuned

http://hyo-hen.web.infoseek.co.jp/yomaigoto/r025.html
http://hyo-hen.web.infoseek.co.jp/yomaigoto/images/m.jpg

I couldn't find video.
But I found two pics.