AmEx Membership rewards transfer 1:1 into ANA. ANA points can be used for a *A award on United or Air New Zealand (I recommend UA's C over NZ's C). Same story holds for Mexicana. UA requires 90k miles for a C ticket, but I haven't seen the ANA or MX *A award charts so YMMV.
You can also transfer 1:1 into Continental or USAirways. I believe both of those allow Qantas redemption options (both require 105k miles for a C ticket), and USAirways should very shortly allow United redemption as well.