We've been to the Canadian Rockies three times. The first time we were there was 2005 for a week in early September. We set out to do the Brazeau Loop (on border of Banff and Jasper, got our permit through Jasper since the backcountry sites are in that park). First night we had a snowstorm and really weren't equipped for it so hiked out and ended up doing some day hikes the rest of the week (Helen Lake and Cirque Peak, Sentinel Pass and Mt Temple, Fairview Mtn, Cavell Meadows).
We learned our lesson and the second time we went back in 2006 we went for two weeks (again, early September). Our weather ran the gamut from sunny and warm to another snowstorm, but it didn't really disrupt our plans too much (we had to cancel our trip into Assiniboine). This time we did a series of shorter backpacking trips: the Rockwall in Kootenay, Berg Lake and Snowbird Pass in Mt. Robson Provincial Park, and Tonquin Valley. We also did some dayhikes - the Iceline Trail and Burgess Pass in Yoho).
Our most recent trip was last year (two weeks in late August). This time we had our ~21 month old daughter with us and backpacking wasn't really an option. However, we still made it into the backcountry. We camped three nights at Lake O'Hara in Yoho and five nights in Assiniboine Provincial Park. We also day hiked (Eiffel Lake/Wenkchemna Pass, Burstall Pass, trails around Lake Louise, Bourgeau Lake).
Out of the backpacking we did, Berg Lake was our favorite (close second was Tonquin Valley). We camped two nights in Berg Lake (day hiked to Snowbird Pass the second day), and one night at Kinney Lake (we could've gone all the way out the third day, but opted to camp in the backcountry instead of car camping). I think it was ~12.5 miles to Berg Lake and about 14 miles RT to Snowbird Pass).
While Berg Lake was our favorite backpack, Assiniboine is our favorite area. We had intended to backpack Assiniboine on our second trip, but canceled due to snow. Last year we cheated and took the helicopter in (17 miles with a toddler and all our gear just wasn't happening, lol). It was just gorgeous. You can arrange a one way hike (17 miles in and 17 miles out), but to forgo the hassle I think most people go in and out the same way. If you wanted a longer trip you could hike in to Assiniboine and base camp for a few nights. There are many scrambles and dayhikes there that are amazing. Another nice thing about Assiniboine is that you don't need a permit for the campground by Lake Magog (run by Assiniboine Lodge and when we called for a reservation they said they never run out of room, so you just roll up).
What we saw of the Brazeau loop was wonderful, we still want to go back and do it. It's supposed to be a great hike. Other backpacks we haven't done that are supposed to be nice are the Sawback in Banff and the Skyline in Jasper.
We used the Patton and Robinson book for planning (I think it's on the seventh edition - considered the Canadian Rockies bible). Another book that people like (we've thumbed through it and liked it, just didn't buy it at the time) is "Don't Waste Your Time in the Canadian Rockies". Depending on time of the year certain trails might be closed and/or hiking restrictions in place due to grizzly activity. We didn't carry a bear canister - the backcountry sites we were at had bear poles for storage and separate cooking areas. Typical precautions recommended for travel in bear country - make noise, bear spray, etc.
Late August was perfect for Assiniboine - the nights were around freezing and there really weren't any bugs. Locals told us earlier the summer the bugs can be horrendous. Likewise, Tonquin Valley is best done late in the season too (lots of horse traffic creating muddy trails and also really buggy).
Our pictures/trip notes are posted here:
2005 (mostly day hiking in Banff)
2006 (the Rockwall, Tonquin Valley, Berg Lake, Yoho day hikes)
2009 (Assiniboine, Lake O'Hara, Lake Louise day hikes)
We LOVE the Canadian Rockies. You will have a fantastic trip. Let me know if you have any further questions -- happy to help!