By world currency I am assuming you mean currencies that can be used by everyone in the world, without translating that currency to that country's native fiat currency.
I don't think Bitcoin will become this though, too many problems such as high transaction fees, but other altcoins might have a chance of this.
Anything is possible, but we still have a LONG ways to go if Bitcoin is to become used by everyone. Still today 99% or more of people do not know what it is.
It's possible if technological advancements were made and the countries adopted it. The problems it has now may be solved in the near future and as of now, a lot of countries are starting to accept Bitcoin and cryptocurrencies.
It would be cool though if it were. It would provide convenience for the travellers, because they won't go through the hassle of having to exchange their fiat money to the local currency of the country which they'll visit and lose a lot of money through the taxes. Also, Bitcoin would allow easy and fast transactions along with the convenience of not having to carry it around. As of now, Bitcoin may look far from becoming the world's currency but it may be possible given the circumstances at hand.