In ArcGIS Desktop, one can add a WMS service where authentication is required. i.e. Someone provides you a secure WMS and provides you a username and password. ArcGIS Online does not offer the same support for WMS services. If it requires authentication, there is no prompt for credentials like when adding a secure ArcGIS Server map service. I do understand WMS authentication is most likely on the web tier, not the service itself, but perhaps there is a way to check for this.
This idea has been merged with Secure WMS Support for ArcGIS Online.
Would be nice to have same type of authentication option for WMS.