Canadian citizens and permanent residents can sponsor their spouses or common-law partners, parents and grandparents, and dependent children.
To qualify as a dependent child when applying for permanent residence in Canada, your child must be under 22 years and not have a spouse or partner.
If your child is over 22 years of age, they may qualify as a dependant if have depended on you for financial support since before they were 22 and can’t financially support themselves because of a mental or physical condition.

You will need to sign an 'undertaking' in order to sponsor your family. This means that you will be financially responsible for the person you will sponsor. For example, if they require social assistance, you may have to pay it back.
For parents and grandparents, there is also the Super Visa program option.