Athabasca Glacier is the most visited glacier in North America largely because it's the most accessible. The Glacier used to run right up to the road where the Icefield Center in Jasper National Park was built. The glacier, however, has been exceeding at an average rate of 16 feet a year, and has lost over half its volume since the start of the 20th century.
To see the glacier up close, you can buy tickets at the Icefield Center to follow a guide up a walking trail for a 3 or 6 hour hike, depending on your preference, or you can take a bus up to the glacier, which will drop you off for about half an hour to wander about and snap a few photos. It's also possible to book day trip tours from Banff.