Archives of Ontario (Toronto) offers a newspaper research guide. The guide includes a list of microfilmed newspapers that are available in their holdings. Note that most of these newspapers can only be viewed at the Archives.
Library & Archives Canada (Ottawa) has a list of newspapers at Library & Archives Canada. Some of these newspapers may be available through inter-library loan.
Many local archives (such as Norwich & District Archives, Stratford-Perth & Dufferin County Museum & Archives to name just a few) have archived copies of local newspapers available for research. Many of these archives require a visit in person but some offer research services.
There are also some Ontario newspapers that have been digitized and are available through subscription services such as Paper of Record and Newspaper Archive. You can view a list of newspaper titles to see if the newspaper you seek is available before subscribing.