Should I stop building a wonder if I find a rival is likely to beat me to it?

Let's say I'm currently building a world wonder, and through my spy I find out a rival civ is also building the same wonder, and are likely to complete it before me, even if I try to rush mine in a variety of ways.

So getting the wonder is nearly hopeless. Should I just immediately cancel the construction and divert my production elsewhere, or should I keep constructing it for the gold reward? And if the answer is "depends", then under what conditions should I choose one way or the other?

If you're say 95% sure that the AI will beat you to completion, absolutely switch construction immediately. The gold to hammer conversion is better than producing gold but it's still a horrible use of hammers. You should build a different wonder or a building to use the opportunity cost of producing something that will help you in the long run. Remember you still get the gold for the production you've already invested whether or not you're currently building that wonder, so it's not wasted production.

Alternately use the production to build units and then go relieve the AI of the wonder that way.

Depends ;)

I don't have the Gods & Kings expansion, yet, but if they didn't change the game mechanics, here is what happens for your options:

Cancel the production:
Pro: You can instantly use your resources for another project
Con: You lose everything you have invested so far

Wait until your opponent beats you:
Pro: You get your invested resources in the form of money
Con: You could've built something else in that time

So it really depends on how long you already have been building on that wonder and how bad you need money. I usually continue building, because extra money is always good for bribing city states or upgrading units.

You should almost always change projects. Hammers which have been spent on a project which can no longer be built are converted into gold one-for-one. This is a bad conversion! The gold isn't multiplied by your gold buildings or policies or anything. Each hammer gives you just one gold.