I gather from all of the replies and links that SPG Amex is a popular choice. By transferring Starwood points to an airline program one could overcome the restrictions imposed by "universal miles" cards, i.e. a requirement to book 14 days in advance, a requirement to have a Saturday stay on the ticket, and a maximum cash value for the ticket.

I have done this with the AMEX Membership Rewards program which is very similar.

However, what I'm really looking for is a NON-AMEX card with that same feature, transferring points to airline miles programs, for use when AMEX is not accepted.

I haven't been able to find such a card.