If you are coming to Canada on a work permit, your family can accompany you if they qualify to enter Canada as visitors. Consult the Canada Citizenship and Immigration web site.
Your spouse (husband, wife or common-law partner including same-sex partner) may qualify for an open work permit without having a specific job offer and without the need for a job confirmation (LMO) from Human Resources and Skills Development Canada (HRSDC) through the Spousal Work Permit Program.
Please note: Regulations for work permits for the spouse/partner of Canadian citizens are different. If this situation applies to you, please contact the Faculty Recruitment and Support Program.
Note: there is no "fiance(e) visa". If this is your situation your fiance(e) will need to apply separately under the Skilled Worker Class, or you may sponsor him/her once the marriage has taken place.
The Government of Canada organization responsible for the rules for bringing pets to Canada is the Canadian Food Inspection Agency.
Their web site provides detailed information on various types of pets.
Assistance dogs are exempt from import requirements when the person who is assigned to the dog accompanies it to Canada. This includes dogs certified as vision or hearing dogs.