Labour law in Canada varies by province but as far as I know, no province requires the employer to pay for sick days. Some employers may still do this, mostly government, city, universities and places like that and they might be paying for 10-20 sick days per year.
Most employers include a benefits package with the job including a supplementary health insurance which might include a temporary disability insurance that might pay something if you are sick. When you apply for jobs, you can ask about their benefits package and if you have more than one offer, that can be a factor in your decision on which to take.
Apart from that, Employment Insurance includes sickness benefits and maternity/parental benefits. In all cases, you have to have worked a certain amount of hours to qualify for that. For parental or sickness benefits, that's 600 hrs. in the previous 12 months. For regular unemployment it is 420 to 700 hrs. depending on the percentage of unemployment in your area. The amount paid is 55% of your gross salary but with a maximum of $457 per week. There is a 2 week waiting period so if you are sick for less than 2 weeks, you get nothing.
For maternity leave, it's true that it's 15 weeks for the mother and then 35 weeks can be split between the parents. For sickness benefits, the maximum time is 15 weeks and for regular unemployment, it depends on how many hours you had worked and the unemployment rate in your area but could go up to 45 weeks according to their table.
You can find more info at http://www.servicecanada.gc.ca/eng/ei/types/special.shtml#Sickness3