If you have an interest in Calgary and area history and genealogy, there are very friendly volunteers on hand to help you during the open hours. However, the library holds much material about all of Alberta as well as the world. Their collection of worldwide Family History Journals is simply impressive!
If you aren't able to visit, they do provide a look up service and research help.
BMD Database - 38,000+ records
Cemetery Database - 197,000 records
Online Data Projects - transcription projects which include: Barr Colonists, Members' Surname Interests, Turner Valley Oilfields Death Index, and Calgary Crematorium records 1937-1979
Newspaper announcements page - transcriptions of Births, Marriages and Deaths from local newspapers, and is linked to the above BMD Database.
Southern Alberta Pioneers and their Descendants - a searchable database
The Research Aids page is worth a gander as the content is good food for thought. For example, looking for a US phone number is very helpful. European History Interactive Map is fun too. Please note that some links may be a bit out of date.