it should be great hiking weather. days will probably be in the low-mid teens (celcius). nights will be cool. best to bring cloths that layer well. if the sun is out it will be nice but if it rains or is over cast, the temps could drop down low. great time to visit the mountains.

September is a beautiful time to visit Banff.
The deciduous trees should be blazing in golden autumn colors; the temperatures will be not hot and not cold. . . ahem!! although it has been known to snow in September!!, but normally won't stay around long, and if it does snow, it is usually at the higher elevations, while rain falls in the valleys. It could go the other way too - there could be a hot spell.
Normal temps range from freezing (or slightly below) at night to about 18C = approx 65F during the usually sunny days.
It should be perfect for hiking.

To augment what the previous poster have told you......

Bring sensible hiking boots, woollen socks, long underwear, sweater, cap, gloves or mittens and a jacket. If you have enough other layers on, then a 3 season jacket should be enough in even the coolest weather September is likely to throw at you.

I like the waterproof, fleece-lined jackets that Lands' End, LL Bean and Eddie Bauer sell. I prefer the slightly longer jacket that covers my butt to the shorter, bomber-style jacket that comes down to my waist only.

But bring a short sleeved T-shirt too, in case the weather is warm.

Restaurants in the mountains are quite casual. In even the fanciest restaurant, smart casual dress is adequate for dinner. In the more casual restaurants and pubs, jeans, chinos or corduroy pants are fine.

Go to www.weather.com, do a search, then click on "averages", then the month you are visiting.

Just before leaving, check the 10-day forecast for finalizing your packing.

Even so, be prepared for warmer/cooler. The weather is SO variable, you cannot even count on the morning forecast on the TV in your hotel room.

Therefore, it's always best to pack the ubiquitous "layers". Along with an umbrella. And, gloves, too, just in case. And, warm socks...

Djkbooks, I agree with all of your advice, except:

>>>>>>Along with an umbrella.<<<<<<

This would be impractical along forest paths, IMO. But I'm glad you mentioned the umbrella, because it reminded me of an omission in my list. Waterproof pants that are worn over regular pants or over long underwear would be a good idea. A hooded jacket also would be a good idea. I think a hooded waterproof poncho would work fine too.

Thank you all so much for your input! It was very helpful.

I was in Banff in mid-September 2002. The people who were leaving when I was arriving had spent the entire begining of the month in shorts and tank tops (or so they said). It very nearly snowed the week I was there. But still hikable.

Prepare for anything.