I recently created an American Airlines frequent flyer account online. Here is one of the oddest parts of the Terms of Service agreement displayed when you open an account:
You must access your account information directly through the Site and not through a third party web site, including but not limited to any mileage management service, mileage tracking service, or mileage aggregation service. You also violate this Agreement if you enable an AAdvantage member to access account information without visiting the Site.
American also requires an account holder to receive monthly account updates by e-mail. Evidently, using web-based e-mail like Yahoo! to look at that e-mail would violate the terms of service, because Yahoo! would be a "third party web site" and reading the e-mail would be "access[ing] [my] account information." So would my habitual practice of directing all account-member e-mails for my partner to a junk e-mail box and then forwarding him the interesting bits.
I would guess that American Airlines might not expect you to read all of their e-mail updates, but I am surprised that they reserve the right to close your account in the off-chance that you do read them.
This paragraph does not appear in the Terms of Service agreement accessible from the website. Perhaps it is only in the "I accept" Terms of Service to amuse people like me who actually read those contracts from time to time.