This really does depend on where you are travelling.

I am a native English speaker and speak varying degrees of German, French, Spanish and Italian.

For most people, I would say that Spanish and French are probably the most useful travel languages (apart from English of course). This is simply because of how widely they are spoken in different parts of the world.

With Spanish, you basically have the whole of Central and South America covered (with the exception of Brazil - and there is enough mutual intelligibility between Spanish and Portuguese that it can be used an an emergency option). It is also understood in many parts of Africa, although not to the same degree as French.

French covers quite a few European countries, a good chunk of Northern and Western Africa, parts of the Caribbean and Pacific.

As mentioned, German can be useful in Eastern Europe - specifically, it has got me out of a couple of tight spots in Croatia and Slovakia - but is much less global than Spanish and French.

As a travel language (as opposed to a business language), I would probably only recommend Chinese or Japanese if you are spending a lot of time in those specific countries, as you will not find them widely spoken elsewhere. For most of Asia, English is by far the most useful lingua franca.

For a native English speaking global traveller, I would say start with Spanish and then move on to French. If you speak those three, you will be able to travel to most parts of the world without major difficulties.