There are no comprehensive lists of immigrants arriving in Canada prior to 1865. Until that year, shipping companies were not required by the government to keep their passenger manifests.
There are individual projects and databases online that may be of help in your search
Shipping Company & Customs Agents Records
There are a few surviving passenger lists which were kept by shipping agents in the originating country. The Passenger Books of J & J Cooke, Shipping Agents gives sailings from Londonderry to Quebec and St. John New Brunswick from 1847 to 1871. These are online at
St. Lawrence Steamboat Co. Passenger Records 1819-1836 at
The Hawke Papers, letterbooks of Chief Emigrant Agent Anthony B. Hawke are also available at the Archives of Ontario. They cover the years 1831 to 1892. See the
searchable database for years 1865 - 1883 at http://www.archives.gov.on.ca/english/db/hawke.htm
Names of Emigrants from the 1845-1847 Records of James Allison, Emigrant Agent at Montreal is online at http://www.rootsweb.com/~ote/ships/emigrants-montreal1845-1847a.htm. This an index only but if you find a name of interest you can consult the published book
There is also the Return of Emigrants Landed at the Port of Kingston Ontario, Canada 1861-1882 which gives the final
destination of the individuals, their date of arrival at Kingston and more. It is found at
Immigration Projects Online
Ships passenger lists for Peter Robinson Settlers sailing 1825 Ireland to Canada are online at http://www.rootsweb.com/~ote/ships/
Petworth Immigrants 1832-1837 at
Emigrants from England in New York City Almshouse 1818-1830
- 254 names of English immigrants to Canada & USA including the name of the ship they sailed on at http://www.allenglishrecords.com/almshouse-a-f.shtml
If you are looking for Irish ancestors, you may want to search the online database Irish Immigrants at Grosse-Île at http://www.collectionscanada.ca/genealogy/022-504-e.html This database has information on 33,026 immigrants whose names appear in surviving records of the Grosse-Île Quarantine Station between 1832 and 1937.
There are search engines to search multiple websites for
ships going to Canada at
They include most ships lists on the Internet going to Canada and the online InGeneas databases for immigration to Canada 1800s
New Brunswick Arrivals
The Saint John Customs House Passenger Lists 1815, 1832,1833-1834 & 1837-1838 are the only known surviving listsfrom this time period. Some can be found online at
http://www.theshipslist.com/ships/passengerlists/saintjohnindex.htm Most of the Customs House records were lost in 1877 in the Great Fire of Saint John. Famine lists from 1845-1850 appear also to have been lost.
There is a mailing list called CAN-SHIPSLISTS-PRE1865-L for queries and discussion involving immigration to Canada before 1865. You can subscribe from this page
TheShipsList website has Quebec ship arrivals extracted from contemporary newspapers.
Library & Archives Canada Holdings
There are a few ship passengerlists pertaining to British-subsidized immigration schemes for the period 1817-1831 and these are available from the National Archives of Canada in Ottawa.
The Miscellaneous Immigration Index is a nominal card index to some of those records and it is available for consultation in the NAC Reference Room. It relates mostly to immigrants from the British Isles to Quebec and Ontario between the years 1801 and 1849. The Miscellaneous Immigration Index has been put into a database, which you can consult on the InGeneas web site.
For immigrants from France, the NAC holds scattered records for the years 1732 and 1749 to 1760. Microfilm copies of these lists are available through ILL - ask your local library for help. You can also consult the NAC microfilm shelf-list for reel numbers.
Miscellaneous Websites with Immigration Information on Shipsto Canada
Immigrants to Canada
The Ships List
Ships Passenger Lists Online
Finding Ships Passenger Lists to Canada
Ships Passenger Lists to Canada 1400-1930