It depends on the province in which you reside.
Here's a chart:

Province/Territory	Minimum Age for Credit Card
British Columbia	19
Alberta	18
Saskatchewan	18
Manitoba	18
Ontario	18
Quebec	18
Nova Scotia	19
New Brunswick	19
PEI	18
Newfoundland	19
Yukon/NWT/Nunavut	19

Of course, these are the ages you need to be just to apply for a credit card, you still may get rejected for one. Don't bother applying for one if you're in one of these provinces and younger than the ages above.

If you're a Canadian university/college student, and have determined that you're worthy of a credit card, I'd recommend applying for the Smart Cash MasterCard® Credit Card, which is one of the best cash back credit cards available that is aimed at the student market. With the points earned, you're looking at a 0.84%-0.87% "cash-back" in the form of gift certificates, and the points earned goes up to 1% if you use it for travel. That's really good for a student card.

If you can't get the Smart Cash MasterCard® Credit Card, I'd suggest applying for a credit card at the bank you have a chequing account with, and it's best to ask a teller at the branch what the best way to apply is.

If you just need to make small purchases with a Mastercard or Visa, or need something a little less debt-prone, check out my article on the Best Prepaid Visa cards and Mastercards in Canada 2012.