FYI, As the previous writers have stated, all services to Singapore (SIA, UA, NW etc) all operate via Tokyo, Osaka or Hong Kong if flying over the Pacific. SIA services from JFK or EWR operate via FRA or AMS (initially it was BRU), then onto SIN. As far as service to Australia from LAX, United, QF & Air NZ all operate non-stop service to Sydney. United operate daily non-stop to Melbourne (at 12,762kms,the longest non-stop service, year round, in the world!) & QF operate 5 times a week non-stop with 2 B747-400's via Auckland. United also operate SFO-SYD non-stop daily, codesharing with Ansett. Apparently the longest in miles is JFK-JNB at 7960miles, operated one-way only.
Hope that helps?
Ansett Australia - (was) One of the worlds great airlines!