For Calgary, it's all about the weather and elevation:
1. Bring a wider variety of clothes than you think you'll need. You'll need a jacket virtually any time of year, but you may also want lighter clothes in April in case we hit 20 or higher. And you may need a winter-ish coat in May.
2. Bring skin lotion. Calgary's dry air wreaks havoc on your skin, especially if you're from somewhere coastal. About the only month this doesn't apply is June (see next point).
3. An umbrella is a must in June (and late May-early July). Calgary, while semi-arid, gets torrential rains for about a 6 week period every year. We call it "monjune".
4. Don't underestimate elevation effects. While you won't typically see full-blown altitude sickness here (unless you have a medical condition), people find themselves easily out of breath even for the most trivial of exercise. Again, especially if you've lived near sea-level most of your life. Also, combine this with the dry air and anyone with asthma or other breathing problems absolutely has to have their meds on them. The other thing is, the sun is a fair bit stronger here. You'll burn faster in Calgary than any other major city in Canada, due to the thinner air. You'll also want sunglasses more often than you're used to.
5. Headaches - depending on the time of year, people sensitive to air pressure changes can suffer crippling headaches. Especially in our chinook months, but this phenomenon occurs year-round.
Wow, it really sounds like a horrible place to live.