Currently, you can transfer your American Express Membership Reward points to British Airways Avios points at a 1:1 ratio. This has been a very valuable transfer partner and from time to time there are actually bonus offers on transferring your points! In my opinion, British Airways points can go very far and has been one of my top transfer partners to date.
Unfortunately though, the transfer ratio is about to change. On October 1, 2015, points will transfer at a 20% devaluation where 250 American Express Membership Reward points will equal 200 British Airways Avios points. This is pretty significant in my opinion as it is a decent devaluation for not only the transfer ratio but American Express Membership Reward points as a whole.
With that being said, if you are sitting on a ton of American Express Membership Reward points you might want to think about transferring them over to your British Airways Avios account within the next week. Of course there is no transfer bonus at the time and one could always pop up, but you never know. I also hate transferring points speculatively as you then lose the flexibility option of those points. Since I transferred over a ton of points during the last 40% bonus opportunity (no longer going on), I am not going to transfer over anymore points speculatively. Hopefully I do not regret this decision, but I have enough British Airways Avios points right now and still want to hold on to some American Express Membership Reward points for the flexibility with other partners.