[Source 2016/8/7:] A transit is by definition less than 24 hours, with some rare exceptions if the best available connection is longer.
If you want to stay longer, you'll need to look for a stopover. These often cost extra (US$100 is typical), although some airlines like Singapore and Emirates offer well-priced stopover packages including hotel, and
usually need to be booked by a travel agency instead of online[emphasis mine].)
[ Source 2013/5/29: ] Second, Air Canada (since you mentioned Toronto) has a special program involving connecting through Toronto, Montreal, or Vancouver and getting a hotel night as part of a package. (Free if you are on a high fare, $49 otherwise.) You also get lounge access at the stopover airport. It's pretty enticing for someone in your situation.
Are there exceptions to the grey above? I would be stupefied if no online search engine can accomplish the grey above?