XKCD creator and Internet Geek King Randall Munroe just published a webcomic that shows how high above 4 North-American cities the ice sheet cover was 21,000 years ago. Knowing Randall's attention to detail, we can be pretty sure that the scale is accurate.
As you can see above, Chicago was relatively spared with only 900 meters of ice (0.55 miles), but Montréal was deep under 3,300 meters (2.05 miles) of ice.
With global warming going the way it's going, ice isn't what threatens us. But it's extremely useful for scientists to look at how the Earth has changed in the past to try to better understand how it could change in the future. It's also good for the lay-person to know about these things because it can dispel the impression that many have that things are pretty static and can't change enough to make life hard for us and many other species.
If you're curious, the source of the data used to make the drawing is "The Laurentide and Innuitian ice sheets during the Last Glacial Maximum"; by A.S. Dyke et. al..