If you are sponsoring a spouse or dependent children, you could be refused as a sponsor if you have been taking social assistance, are bankrupt, have a criminal record for violent crime, are still bound under a prior sponsorship, have defaulted on your obligations for a prior sponsorship or owe alimony or child support, see http://www.cic.gc.ca/english/immigrate/sponsor/spouse-apply-who.asp
If you are sponsoring another relative, you could also be denied if you do not make enough money to support your own family plus the people you are sponsoring. Go to http://www.cic.gc.ca/english//information/applications/guides/5196E10.asp and look at table 3 to see how much money you have to make for the total of your family plus sponsored persons. You can have your spouse co-sign sponsorship of other relatives in order for the spouses income to count too.