Trail Runs 
Road Runs
Trails
Aylmer Lookout
Bourgeau Lake
Cascade Mountain
Fenland Trail
Lake Minnewanka
Lower Stoney Squaw
Mount Rundle
Mystic Pass
Rockbound Lake
Rundle Riverside
Sulphur Mountain
Tunnel Mountain
Vermilion Lakes
Links
Overview
Trail Running in the backcountry is a lot of fun but not without certain dangers. In the Banff area you may well encounter bears and other wildlife.
In addition there are many hazards on the trail from loose rocks and roots to snow and ice. Many routes listed here involve serious elevation gain and some routes like Rundle and Cascade have seen a number of deaths over the years.
As with all backcountry travel, a little preparation and a good dose of common sense can save you a lot of trouble in the long run
Before You Go
Make sure that you leave clear details of where you are going, who you are with and when you expect to be back. It is better to write this down somewhere rather than rely on others to remember what you said. Once you have left that information do not alter your plans without letting someone know. It can feel a little restricting sometimes to have to run where you said you would, but it is better than having a search party looking for you in the wrong place.
Take water, food, warm and windproof clothing, cellphone (turn it off and keep it for emergencies) and bear spray along with a small first aid kit. This should be your basic kit that you grab every time you go out. Once you have things organized it is as simple as grabbing your fanny pack or Camelback and running out the door.
Hydration
For any run longer than about 45 minutes you should definitely take your own water supply. For runs up to an hour and a half I'll take a water bottle in a fanny pack. For the longer runs I don't leave home without a hydration pack with 100 ozs of liquid.
While there are natural water sources available on some routes I prefer not to rely on them, you never know when an elk with diarrhea may have passed through :)
Wildlife
If you run the trails around Banff then you need to be prepared for wildlife encounters.
First rule is if you can avoid a wildlife encounter then both you and the animals will win.
Before I go for a run I always check Trailex for the latest animal sightings. If there's been recent activity where I am planning to run then I change my plans. Of course just because a bear was in place A yesterday doesn't mean that it won't be in place B today but it helps to have an idea of where the hotspots are.
Next step is to carry bear spray. It isn't cheap (~$40) a can but it can save you're life so don't be dumb. There are local stores which will rent you a can for a few bucks so make sure you are equipped should things turn bad.
Make lots of noise on the trail, sing whistle, clap, holler, whatever suits you, just make sure that you don't suddenly run into a bear that didn't hear you coming. I read a report of one guy that ran all the way up and down Cascade Mountain and ran into a bear in the parking lot so don't just assume that a bear encounter will occur 20km into the bush.
Weather
Changeable would be the best way to describe the weather in the Rockies. It is not uncommon to see snow at some point in every month of the year and just because a day starts out sunny it is no guarantee that rain, snow, thunder and lightning will not follow. Be prepared with rain gear, appropriate warm layers as well as sunscreen and bug spray. You may need all of it on the same run. Don't try to be a hero, if you are taking on one of the bigger mountains and you sense that the weather is changing for the worse, then turn back and come back another day. One hour up a mountain can be many hours down if the weather turns bad.
Clothing
Don't run in a cotton T-Shirt! Just don't.
The best advice is layers and go for good wicking materials. In the height of summer I'm running in a Coolmax T-Shirt and Bike Shorts, good wicking socks and that's about it. I'll also have my trusty Goretex Windstopper shirt that can shut out just about anything and it's a good idea to have a lightweight pair of pants in there somewhere too. If you're doing something long (2 hrs +) then an extra pair of socks may save you should you take a dunking.
Footwear
Make sure you have a good pair of Trail Runners (they are different from road runners with more torsional stiffness). You can run some easy trails in road runners to get an idea if you like it but really you should invest in some proper trail runners if you start to get into this crazy sport.
If you don't know too much about it then head to a local running store and find someone who actually runs trails. If you can't find anyone then go to another store. It is a specialized sport and you really need to find someone who knows what they are talking about.
Reading
If you're interested in running trails in the Banff area then you should pick up a copy of The Canadian Rockies Trail Guide by Brian Patton & Bart Robinson. My general rule of thumb is that if you can hike it then you can run it and this book is the classic guide to hiking in the area and a great starting point for your explorations.
If your adventures start to take you up to the top of mountain peaks then you will probably want to pick up Scrambles in The Canadian Rockies by Alan Kane.
If you plan to do Rundle or Cascade then make sure you stop into the Parks Information Centre at 224 Banff Avenue and pick up their excellent (free) guides on the two mountains. While you are there you can check the weather reports.