As a world language, English is in the lead right now. But in the Middle Ages, the lingua franca (at least in Europe) was Latin. That's a big part of why English has so much Latin in it! (...The other part being England's rule by a French aristocracy in the early days of English.) In Central/South America and Africa, Spanish, Portuguese, and French, all three of which used to be dialects of Latin, are also major contenders. Australia, the US, and Canada all speak English, which is also a widely spoken official language in India.
We've covered the Americas and the southern hemisphere, and so far it's looking like some form of English or Latin is the best candidate. So what's left? Mostly just Eurasia. I may be wrong, but it's my current understanding that English is the language to learn all across that mega-continent, the de facto lingua franca. So if there's going to be some conscious effort to push a single existing language as the default language of business, science, politics, and such for the entire world, I'd say English is the obvious choice. But what sort of English? Even deciding between the American and British dialects is problematic. It seems to me that neither one is acceptable.
Anyone who's ever tried to study or teach English knows that its sound system is overly complex (especially the vowels), its grammar is far from consistent, and it has at least two words for almost everything: one Germanic and one Latinate. An obvious remedy to all these problems is to define an artificial dialect of English expressly for use as a world language. The most important motivation for this is reducing the time and effort required to learn the new language. When choosing between redundant vocabulary items, those coming from Latin (or any Romance language such as French or Spanish) should obviously be favored to facilitate maximum comprehensibility.
Additionally, this new form of English should be even more open to foreign borrowings than English is already. To get this rolling, all major world languages should be scanned for popular borrowings already in use in more than a few of them. These useful words could then be listed in the official definition of World English.
It's important to remember that this constructed dialect of English would not in any way be a replacement for anyone's native language. You don't teach your kid World English instead of whatever language you naturally speak; that's ridiculous! This is the sort of thing that could be learned in middle school, high school, or even college. Not everyone even needs to learn it; it's just a go-between language for people who travel a lot or have frequent dealings with speakers of foreign languages. For those people (an ever-growing segment of the world's population), some form of World English would be a big help.
If you're interested in this topic, check out this World English website for loads of good information both on what English is and on how it can be used as a world language. To see some more arguments on both sides, here's one article claiming that English is not going to become a world language and another claiming that it already has! Actually, they really don't disagree too much: English is very important globally, but it's not going to wipe out other important languages like Spanish or Chinese.