The North of Canada is extremely cold and inhospitable for human survival, at least not without a huge and disproportionate input of resources. If you look at population maps of Canada, you can see that the most densely-populated areas are further south and are more temperate. While I'm sure there are other reasons for Canada's lower population, the climate is certainly a big influence.

Climate. Pure and simple. Much of Canada experiences extreme cold temperatures that make living difficult. The vast majority of the US is much more temperate. Take a look at the Population map of Canada. Most of Canada's population is pressed up against the US border in regions that have more moderate temperatures.

The climate of the United States allows for an amount of agriculture that isn't possible in Canada. Table of agricultural land of select countries Canada when compared to the United States has relatively few viable types of crops. Crops like Tobacco and Cotton won't grow in Canada's climate while nearly all crops grown in Canada can also be grown in the United States. This historically gave the US has an economic advantage that helped spur growth.

The availability of farm-able land was enormously important to the growth of the United States. 150 years ago nearly half of the US population lived and worked on a farm. 37% of US GDP was from agriculture. Interestingly Canada's numbers are very similar percentage wise to the US but with only 1/8 the land available for agriculture.

Of course there's more than just agriculture to worry about. Canada's extreme cold requires a great deal of planning, effort and even some luck to survive. One great example of how the cold may have influenced migration is the gold rushes of the 19th century. About 300,000 people went to California for the California gold rush but only about 100,000 went to the Northwest territory for the Yukon gold rush. There are of course many reasons for the difference in participants but one major factor is that in winter a man without shelter in California is cold and a man without shelter in the Yukon is dead.

Canada and the US aren't unique cases of population density. Throughout the world places with extreme climates that don't support agriculture have relatively low population. Take a look at a Map of the world by population density Northern Canada, Siberia, Patagonia, the Sahara, the Gobi, Greenland, the outback all of these are places where climate has inhibited the population. The simple fact is some places are better suited for humans to survive. The United States as a whole has a climate better suited for human survival than Canada.

For Canadian agricultural statistics visit Statistics Canada Section M: Agriculture

US agricultural statistics warning PDF

This would be more of a Geography question, but since that's what I'm studying and I happen to be in the library I'll take a crack at it. My source will be "Geography: Realms, Regions, and Concepts 2000" since that's what's available.

First off, as VOZ pointed out, most of Canada is not hospitable. According to the text, only 1/8 of Canada can be classified as habitable.

I would say another factor not listed in the text is the lack of harbors on the eastern shore. While the United States has many good options, I'm not sure Canada does. Besides the St. Lawrence river giving access to a few areas, there isn't much else.

The text also lists the physical barriers of the Canadian Shield north and west of the Great Lakes, and the rugged highlands separating the Great Plains from the Pacific.

Finally, I'm sure someone could make an argument about the French and the British having some historical difficulties and not caring to settle it further, but that's outside my knowledge and I'm not sure if that actually contributed to the lack of settlement.

There are a few reasons, including climate. The first colonists of Canada were the French. They established New France. The main industry was the Fur Trade. The population grew around the main areas of Quebec City, the Saguenay, and Montreal, but not anywhere else. Where as the English Colonies to the south expanded west for farming and ranching, New France discouraged immigration and expanding outside the main population centers because it would effect the Fur Trade with the native populations. New France was Catholic and New England was Protestant, so they did not get along and there were constant raids. There was little cooperation and much distrust so trade was not widespread which might have also encouraged expansion. The British also owned the interior of Canada, then called Rupert's Land. They also discouraged settlers in that area because they monopolized the Fur Trade through the famous Hudson's Bay Company. Certainly, despite the climate, Manitoba and Saskatchewan offered superior farm lands, but as proven with Lord Selkirk and his attempt to build a colony near the town named after him, the British weren't supportive. So, several factors are at play: the climate, the isolation of New France because of ideological differences from New England, and the emphasis on the Fur Trade rather than expanding settlement in the west are the main reasons for Canada's smaller population.

EDIT: spelling and grammar.

EDIT: Also, after the American Revolution, free America allowed for much more expansion without British control.

I would agree with most of these answers, but I want to expand on them. While climate has played probably the biggest role in this phenomenon, it is geography more generally which is really responsible. This article, though it attempts to answer a different question, sheds light on some of the more subtle differences between the countries' geopolitical potential:

http://www.stratfor.com/analysis/geopolitics-united-states-part-1-inevitable-empire#axzz3OdWuZGdy

Some highlights:

The Canadian Shield, while cold, has also been stripped of most of its topsoil by eons of glacial movement.

The rivers. No one talks about the river network that spans most of the eastern United States but this article focuses on it. The navigable river system makes shipping goods significantly cheaper, among other things. While it has plenty of rivers and lakes, Canada has never had and never will have an inland waterway crisscrossing its heartland.

The Great Lakes. Kind of a tangent of the river network point made above. Through New Orleans via the Mississippi and its northern ports, the U.S. effectively controls both North-South shipping and the Great Lakes region. Even though Canada paid for most of the development of the Great Lakes waterways, it is the U.S. which reaps most of the economic benefit.

Ports, etc. Aside from the St. Lawrence River the U.S. controls pretty much every geopolitically important point on the North American coast.

Edit: just to expand on this a little bit. I was thinking about it the other day and rivers really seem to me to be the single most significant geographical factor in population density. Two new examples to further my point: Australia is the 6th largest country by landmass and has a warm climate but it is very sparsely populated because most of its interior is semi arid or desert. Meanwhile, China is one of the most populated countries on earth largely because of the economic benefits of several large, integrated river systems, even surpassing those of the U.S.

The St. Lawrence Valley and Southern Ontario were settled in a manner that parallels the initial settlements of the American colonies. The St. Lawrence is surrounded by very fertile farmland. Even today, the cities along the waterway compete with cities in the Northeastern US with respect to population and economic development.

The real trick is the Canadian Shield. Think of it as an enormous boulder, half the size of Canada, plunked down between the St. Lawrence Valley and the Prairies. It stretches from Labrador in the east, south to about two hour's drive north of Toronto, then northwest to the sub-Arctic.

The land is either rock or muskeg. Essentially the only economic activities it supports are trapping (which was the primary economic endeavour of European settlers on the Sheild), mining, and logging. None of which require or draw large bases of population.