All nations have an official language that defines who they are. The United States is an predominately English speaking country; a majority if you would. As a nation we should adhere to one language only and not be forced to chose between two or more, or have to learn a second language to communicate within our own boarders.
The United States is a former colony of the British Empire which automatically makes us a part of the Anglosphere (we also happen to be largest contributor to the Anglosphere). Not only that, but we are also one of the few former-British colonies out there that actually predominantly speaks English. Much like Canada, Australia, New Zealand, Ireland, and of course, the United Kingdom.
It makes no sense why we have no established official language when we really should. I already foresee arguments that the absence of English as an official language at a federal level entitles some residents linguistic liberty and it is obvious to me that this is pointed at Spanish. But let me tell you right now that Spanish will never become as useful as English. Ever. It's different for fellow first world countries who happen to be bilingual, such as Canada, Switzerland, Belgium, or even Spain to some extent because all of their second (or third and fourth) language speakers are centered around a specific region where they make a majority, while Hispanics are more spread out and tight in numbers. Therefore it wouldn't make sense for Spanish to ever overcome English. The argument that Spanish will overcome English in the United States is like saying Arabic will someday overcome German in Germany or any other language in a European country.
Sorry I got a bit off track. Anyway. English must be the official language so those who immigrate here (both legally and illegally) feel more pressure to learn our language. Remember this, friends; the U.S. doesn't need immigrants, immigrants need the U.S. and no matter where they come from, if they come here, then they will have to integrate into our century-old anglophone culture. I know that sounds super conservative to say, especially to my fellow liberals, but that is what I have to say
We are suppose to be a diverse country that accepts people from all over the world. So it stands to reason that people who don't speak English shouldn't be forced to learn the language just because the primary language was the language used by the people who forced the people who spoke the native language out (or more specifically into, smaller and not as good lands so that they could get richer)
So if we were to use as single language that every one has to speak, it should be ether one of the native languages, that was used by the people who specifically lived in this country for a longer period than us whites, or it should be our soon to be owners, the chines, or latten which is a much more particle and easier language to learn then English.
Instituting English as a national language is not feasible nor respectful of other cultures. In Europe most citizens, speak more than one language. Since Europe's countries are relatively small, they have several that border with languages than differ. English as a national language is rather egocentric, and attempt to make everyone the same without regard to cultural differences.
English is derived from several other languages including Anglo Saxon, ancient Norse, Latin, and French. This creates several ways of making the same sounds or meanings as well as many idioms that few understand. This creates one of the hardest languages to learn. There are many people who don't speak or understand English. For these reasons I say no.
I take from the answers, you are referring to the US. I will speak on that, though it will be coming with a bit of a Canadian slant, sorry. Up north, English & French are both considered equal official languages. I have a bit of an issue with the two chosen. I would think the First Nations (Native Americans) should have an official language as well (though it would have to be an artificial pan-native language as there are hundreds of native languages in North America. The other option is to just be lazy and inconsiderate of the First Nations and make the two official languages English & Spanish (at least two of the US states have a history with Spain going back to the 16th Century - older than even the English). Just my two cents (well 5 cents since there are no pennies anymore ;)