As far as E-tickets are concerned it'll be a maximum of 16 sectors. If you have a surface sector or arrive into one airport and depart from another, ie JFK/LGA, the ARNK bit counts as one sector !
AA is just preparing for end of 2007/beginning 2008 when all paper tickets will be done away with if e-ticketing is permitted. Which means that everything may be restricted to 16 sectors when you issue a RTW ticket. You may add on as you travel, but I don't know how AA or other oneworld partners will handle this - but I think it will be problematic no matter how simple the airlines want you to look at things.