Canada's "Wild West" was very different from the American. Partially this was a matter of geography: to a Canadian of the era, the "West" meant anything west of Lake Ontario. Between the lakeshore and Victoria, British Columbia was a vast expanse of territory that was still almost entirely tribal, only intermittently punctuated by white fur traders missionaries. Until 1870 most of the western prairies was owned by the Hudson's Bay Company, and their policy was heavily against settlers. Even bridges were discouraged; making traveling too easy might lead to immigration!

You can count the number of exciting stories of those days on your fingers; there just wasn't the population. Occasionally there was some interestingness, particularly in the form of American liquor smugglers crossing the border (a border that was, at the time, more theoretical than practical). These smugglers built pretty serious fortifications to protect themselves from the limited arm of the law, as well as vengeful native. Fort Whoop-Up, near today's Lethbridge, was the most famous of these. The Northwest Mounted Police (today's Royal Canadian Mounted Police) were formed largely to prevent this sort of whiskey peddling and to enforce that almost-theoretical sovereignty on the prairies.

As /u/jcaseys34 mentions, though, there were gold rushes. The story of the Yukon Gold Rush is an interesting one, but in actual Canadian territory there were almost no instances of Wild West-style gunplay and vigilantism. Most of the criminal offenses were either government corruption or tolerated by the authorities in a sort of "miners will be miners" spirit; Sam Steele of the RCMP was a very practical sort of policeman in this spirit. There was still a very Protestant ethic covering the whole community, though: stories of prostitution being quietly permitted but nobody could work on Sundays, that kind of thing.

The Fraser Canyon and Cariboo Gold Rushes, on the interior of British Columbia, was a bit more rough-and-ready and had more of what you might call the "frontier spirit". There was also an element of national sovereignty involved there, too, as both (particularly the Fraser) drew large numbers of Americans into what was only very, very tenuously British land. Law enforcement resources were thin or non-existent. But when he could, Governor James Douglas held a firm hand and any sort of "wildness" was relatively short-lived. The population of those gold rush towns dissolved once the rushes themselves were over, and the opening of the Canadian Pacific Railway in 1886 ended the whole era: from then on Canadian civilization would develop in leaps and bounds, spreading out from that railway and the two other lines eventually driven across the prairies.

In general, though, the Wild West era in Canada was anything but wild over a very, very broad "west".

People headed west to look for gold in Canada as they did in the U.S. The first gold prospectors went into the Yukon in 1874, and the Klondike Gold Rush began when gold was discovered in the Yukon River Basin in 1896. Between 1897 and 1899, tens of thousands of people headed West into Canada, a task that was possibly even more difficult than going into the western United States. Many of these prospectors ended up in the newly found town of Dawson City, which at the height of the gold rush in 1898 was home to an estimated 16,000 people. One of the most well-known men that went on this journey was author Jack London, whose literary career was saved by the stories he wrote about these adventures and sold.

The Klondike Gold Rush was never really of the scale of some of the western migrations in the States, all in all it is estimated $29 million worth of gold was found in Klondike between 1897 and 1899. The gold rush also greatly advanced the development of the Yukon Territory, which became official under Parliament on June 13, 1898.

Do you mean what was the canadian equivalent of 'the wild west'(if there is such a thing)? Or do you mean what was going on in Canada during the time period where the 'wild west' was happening in the US?

Correct me if I'm wrong, but isn't the idea of American Wild West incredibly glorified through literature and cinema? Meaning that both "Wild West" times in America and Canada are probably similar stories of conflicts with the natives, gold rushes, freedom from government, etc., but not on a big scale as everyone thinks it is.