The specific information you need is covered in B-090 GST/HST and Electronic Commerce, specifically section V, subscriptions to databases and web sites.
The Government of Canada gives an example of charging for access to an interactive web site, and says specifically:
A supplier makes a Web site featuring digitized content available to
subscribers, including information, music, video, games, and
activities, whether or not developed or owned by the supplier. The
subscribers pay a fixed periodic fee for access to the site. The
principal value of the site to subscribers is interacting with the
site while on-line, as opposed to getting a product or services from
The subscribers' right to access the content on the Web site is a
supply of intangible personal property. In essence it is a supply of a
right to use software, and the right to access other digitized content
on the Web site. Although a copy of a digitized product is not
provided, there is a supply of a right to view, access or use a
product while the customer is on-line. As in Example 14, any human
involvement occurs behind the scenes in establishing and maintaining
the Web site, but there is no human involvement on the part of the
supplier when subscribers access the site and its digitized content.
(I snipped a bit about advertising). Thus, your case would be that you are supplying intangible personal property. Intangible personal property is zero-rated, according to GI-034, if you are exporting it to non-registered non-residents (e.g. U.S. residents). That document explicitly states:
Examples of supplies of IPP that will now be eligible for zero-rating
under the proposed provision include:
subscriptions to Web sites that provide subscribers with a right to
access and use digitized content on the site, such as information in a
database or images, and that may also include a right to download a
copy of the digitized content;
subscriptions to interactive Web sites
that provide subscribers with a right to access and use digitized
content, such as games, music and videos, on the sites while they are
My understanding, then, is that you would not charge GST or HST to your U.S. customers, but do need to do so to your Canadian customers.
As always, note that I am neither a lawyer nor an accountant. You will want to consult with one or both to ensure the information as I presented is accurate.