There are a wealth of sources for country profiles. GMID is the best all-around source for information about many countries, their markets, and your potential customers. Business Source Complete has good reports about larger countries. Country Commercial Guides and the World Bank's Doing Business in... series include regulations about exporting and other issues important for planning entry to a specific country's markets.
For specifics about a product, industry, detailed country information such as politics or economic conditions, or information about consumer segments within a country, often browsing through the results of a quicksearch is the best way to go.
COUNTRY REPORT: Enter the country name and the term Country Profile into the quicksearch box.
PRODUCT REPORT: The quicksearch for a country and product pulls in a wide variety of reports and statistics. Click here for a screenshot of results from a search for China beer. Please note: This is the best way to find local competitors.
Be careful what you call it. In this resource, some terms will be more like British than American English; so try different words. For example, take out food in China is tagged home delivery/take away. And what's the take out favorite in China? Pizza! Click here for a screen shot of a category briefing for home delivery/take away food in China.
LIFESTYLE/DEMOGRAPHIC REPORT: To get a wide range of items with demographic and lifestyle information for your country, enter the country name and the term lifestyles into the quicksearch box. Here is a screenshot of results for China pointing to the main report about demographics. (You can see more by increasing the screen to full size and using the scroll ribbon to view the top and bottom of the screen.)
Using the Tree Search (from the landing page or from the category tabs in the top tool bar) gives very complete results. Here's a screenshot showing the tabs, the quicksearch box, and other starting points. A Tree Search requires you to make a number of preliminary choices that you may not yet be ready to make (you must choose a category within the industry, select historical information versus predictions, select a geographical limit -- from the world to Western Europe to a specific country -- and so on).
Market Research Library (U.S. Commercial Service): Use this database to find Country Commercial Guides, an excellent source of both trade regulations and tips about how to position a product to appeal to people in that country. Here's what's available on a typical table of contents.
Business Source Complete contains citations, with much full text, to articles in business magazines and academic journals. For a country report, enter country name (e.g. India) and keywords "country report"
Doing Business in ... (World Bank): Locate a report to 1) download the entire report; 2) search by city or 3) get a snapshot of aspects of the business environment from taxes to gender of owners, workers, and managers of the local competition.