There are two big ways by which increased global temperatures can
cause the sea level to go up. One of them is the melting ice. You're
right that the submerged ice takes up roughly the same amount of space
after it melts as it does before. (Actually it takes up less, but since
most icebergs are partially above water, it comes out about even.) But
not all ice is floating freely in the ocean. There is a large amount of
ice sitting on top of the Antartic continent and Greenland. As that ice
melts, it drips down into the ocean, raising the sea level.
The other way that the sea level rises is because of the
temperature of the ocean itself. Warmer water takes up more space than
cooler water. It's not usually a big enough difference to matter much,
but the ocean is so incredibly deep that it is actually very important.
Between these two things, if the planet were to warm up enough, the
ocean level could rise by as much as several meters. That may not seem
like a whole lot, but it would be sufficient to put a number of
islands, coastal areas, and even some cities under water.
(published on 10/22/2007)