Ships Lists - also referred to as Passengers Lists - were a listing of individuals who were passengers on a particular ship. These lists can be used to confirm your ancestor's immigration to Canada from another country. They may also help pinpoint your ancestor's place of birth as well as other family members.
Before attempting to locate a passengers list, you need to know the following:
Port of departure - where they boarded the ship that brought them to Canada. Knowing the actual city is helpful, but even just knowing the country of departure can narrow down the search. Keep in mind that some ships stopped at several European ports before heading West, your ancestor may have boarded at the 2nd or 3rd stop and not at the original port of departure.
To find the above information use other genealogical resources available for Ontario research. Census records can give an approximate date of arrival (for example if you find your ancestor in the 1861 census but not in the 1851 they may have arrived in that 10 year period - BUT don't assume this just because you can't find them, they just may not be in the area of Ontario where you think they should be). If you can find your ancestor in the 1901 census it may list the year of their arrival (use this only as an approximate - you don't know who provided the enumerator with this information).
Once you have this information, you can check on the availability of passengers lists for the year and port of departure and/or arrival of your ancestor.
If you have an Ontario ships list please consider sending it in to be included as an example.
Passenger lists for ships arriving in Canadian ports prior to 1865 were not archived and most did not survive. The National Archives of Canada has in their holdings Passengers lists for 1865-1935 on microfilm. You can view the microfilm at the National Archives of Canada, at any public library in Canada that has inter-library loan, or at any LDS Family History Centre worldwide.
Not as a whole, no. There are some ships lists available online. Those OntarioGenWeb knows about (ones that include ships headed for or from Ontario) are linked below.