In 1844 18,330 immigrants arrived at the port of Montreal - and that's just ONE port, so imagine how many arrived at all Canadian ports in total.
Before 1865, it wasn't mandatory that passenger lists of ships arriving in Canada be kept. So you may find a few stray lists, or shipping company records - such as the JJ Cooke Shipping Records online at http://olivetreegenealogy.com/ships/jjcooke.shtml
These are sailings from Londonderry to Philadelphia, Quebec, St. John,New Brunswick, and Louisiana from 1847-71, or shipping agent reports like the Hawke Papers, Records of assisted passage, and so on.
There are other records that can substitute for a passenger list. For example, TheShipsList.com is extracting newspaper reports of arrivals and also listing names of passengers who took steamboats once they landed. In many cases you can consider yourself lucky if you find an ancestor on one of these lists!
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
http://olivetreegenealogy.com/ships/kingston1861oct-1862may.shtml These may have your ancestor's name travelling inland once he or she arrived in Canada.
Here is an example of the variety of records that fill in the gaps of pre 1865 Canadian passenger lists ---
Nancy Boggs, 39, Sarah Boggs 17 and Eliza Boggs 14 were listed, along with several others, in a letter that A. C. Buchanan, Chief Agent in the Quebec Immigration Office sent on 19 June 1846.
He prefaces the list of names with "the undermentioned person have been sent out by the Londonderry Union and I have paid them here a sum equal to 10/Stg. each. They are well recommended and the entire of them young and old are well conducted and may be safely employed as servants."
There is more, but this is just an example to show that if you happened to be looking for Nancy or someone else in that letter, you'd be very lucky to find this much!
So, hoping I haven't discouraged anyone - here's two URLs for Ships arriving in Canada