Most companies study their own sales figures first and foremost. They track those figures to look for trends and to see what is working and what is not. They study those figures to determine who is buying their product and build a profile of the targeted customer.
When you fill out the registration card for a camera or lens, you are helping them with their research. Years of experience gives them a good idea of what percentage of users actually register the product and the profile of those users.
Opinions are nice, but what really matters is what prompts a customer to open his or her wallet and that means looking at hard sales figures. Sales figures don't lie. Surveys do (or rather the people being surveyed do).
As for their competitors, they parse any available industry reports to see what the competitors are doing and to get clues as to what they may be doing in the future. Since these are publicly traded companies, they can check the documents that each must file with the respective regulatory agencies in the countries where the companies' stock is sold.
In the internet age, I am sure Canon and Nikon track the Amazon rankings and similar reports for competitive purposes. They have a distinct advantage over the rest of us, because they know how many units they have shipped/sold to Amazon. For example, if the D800 has an average ranking of #7 and the T3i has an average ranking of number #6, while the 5DIII has an average ranking of #8, they can pretty well pinpoint how many D800 units Amazon is selling.
They know what percentage of their total units are shipped to Amazon, so they can extrapolate what percentage of total units Nikon is shipping to Amazon.
That's just one tiny example. Bottom line though, is that the most important data they get is from sales.
With the high-end products (1Dx), Canon knows quite a bit about their customers and may have established personal relationships with many of them. As Mt. Spokane points out, some of these customers may even have a contractual relationship with Canon that allows Canon to access their opinions on the latest equipment Canon is developing.
With a new product, they may do focus groups. With a mature market, like DSLRs, they pretty much know what the customers will buy.
I give Canon credit. It appears that with the 5DIII they did some very focused research because the camera seems well targeted to wedding and event photographers. Just judging by the comments on this small forum, it seems that people who make their living shooting weddings have been very pleased with the 5DIII. A sign that they did some well-focused market research.
As a general rule, a forum like this is going to be about the last place a company looks at for research. Why? Well one of the cardinal rules of research is that you do not want the subjects to self-select. To be accurate, research of any sort requires that the subjects be selected randomly so that everyone in the target universe has a roughly equal chance of being selected. A forum audience is hopelessly skewed and is never going to be representative of the mass of users.
On the other hand, they very likely do conduct some type of "Google Alert" type monitoring to get a sense for what is making its way across the internet. For example, if they find that on 500 photography forums there is a sudden spike in the terms "Canon and White Rubber Grip" they know they have an issue that needs to be addressed. But, as far as reading individual posts on this or any other forum. Highly, highly unlikely.