One of the most difficult parts planning a round-the-world trip is figuring out how to cross the Pacific Ocean. If you have a big budget that's not a problem, but if you're trying to save each penny it could be the most expensive part of your trip.
To answer my question, let's assume we are in Australia or nearby countries and want to get to any country in American continent (North or South America). We can fly or take any sea transport. What's the cheapest way to do it?
NOTE: I've put the "stable" adjective to ensure that the answer will refer to a stabilised route with a non-volatile price, it is, it's not an special offer, a route-code trick or something similar. In other words, it means that anybody can find this price or similar any time.
Given all this, my best price is to fly from Sydney to Honolulu (Hawaii) and then to Las Vegas:
SYD-HNL from ~$400 HNL-LAS from ~$200