Will my child be bilingual?

My husband and I both want our child to speak our (different) mother tongues, but we speak to each other in English and we live in a place where a fourth language is used -- what should we do? 

Most people who learn more than one language do so because they need to. Languages are worth learning if they are some use. That use can be practical, or emotional, or (for adults) aesthetic. If people need to learn a particular language, they generally will. Children are no different to adults in this respect. (Professor Ruuskanen also discusses this fact.) You can expect your child to learn a language if the child thinks it's some use.

It's crucial to examine your situation and decide what language is most 'at risk' in your family. If you live in a place where there is a clear dominant language in the society, which is the language of the children your child will be playing with, or which is the language of education, you can be sure your child will learn that language. YOU don't need to worry about it at all. If you speak a language that is not used much in the community you live in, and especially if you use the dominant community language with your partner, you are going to have to work hard to develop your child's skills in that language, especially if you and your partner speak in the community's dominant language.

And if you live in a place where there are lots of people who speak the same two languages, and where the child is exposed to Language X, Language Y, and all sorts of mixtures of X+Y, then you can relax. The chances are that the child will learn both of them. This is the usual experience for (for example) people growing up in educated families in Delhi -- they'll hear lots of Hindi and lots of English (and in some families lots of some other language(s) as well) and grow up with both, like most of their friends.

Will bilingualism affect my child's intelligence? Is it true that only highly intelligent people can learn more than one language? 

Bilingualism certainly does not decrease intelligence and probably doesn't increase it either. There are bilinguals of all degrees of intelligence, just as there are monolinguals of all degrees of intelligence. And anyone able to acquire one language, even if they are far below average intelligence, is able to acquire more than one language.