You will hear stories of bears strolling down residential streets and such. Most of the time you would not think twice, but if you look closely, the trash cans are all bear resistant, so they must have bears with enough regularity to warrant that sort of expense. I personally didn't see any bears in Banff, though locals said they did see them often enough.
When our bus was coming into Banff in the late afternoon we saw deer cruising down residential streets a few times. Imagine the surprise when we are pulling into the parking lot of the HI Hostel, which is a bit away from center...and we see this beautiful elk very casually munching on the grass. He was used to having his picture taken apparently, he barely reacted to the suddenly crazed tourists who had never seen wildlife so close.
Fondest memory: Waking up seeing the mountains covered in snow. The setting was beautiful
Favorite thing: Elk and deer have the run of the town. It is easy to spot the elk in the mornings and evenings as they find grazing along the sides of the road, in a park or on the Banff Springs golf course. We were lucky enough to see a mother elk and her yearling which was quite insistent about getting some milk from mom.
Fondest memory: Look! The Bighorn Ram! For someone like me who's been living in the city, this is indeed a rare sight! Have never even heard of all the exotic names of these wildlife before coming here! Moose?! Bull Elk?! Caribou?! Pika?!!! To see them in person? WOW!