I´ve been talking to my danish professor and it seems, that "behøver" (meaning: need) is not used at all. Instead, danish people say " jeg har bruge for" or "jeg skal bruge"
I will have to disagree with your danish professor. = Jeg behøver at være uening med din dansk forelæser.
Sometimes I think the word "behøver" must be used instead of "bruger", in other cases it is possible to rephrase a sentence so either "behøver" or "bruger" can be used. I can think of an example with "behøver" that I cannot rephrase with "bruger". Det behøver du ikke. = You don't have to do that. I might use that if I had a guest that started helping me with cleaning up and I felt uncomfortable with them helping me.
Or another example I picked up from a danish dictionary web page that I can rephrase: Jeg behøvede ekstra timer for at følge med i klassen. = I needed extra lessons to keep up with the class. In this case I could rephrase it as follows to use "bruge". Jeg havde brug for ekstra timer for at følge med i klassen.
In general I would say that "need" is tranlated as "behøver" when the meaning of need is more like a requirement, and "need" is translated as "bruger" when the meaning of need is more like "use (for)".
The danish dictionary page for "behøver". http://ordnet.dk/ddo/ordbog?query=behøver
I will try and translate explanations from the web page for when to use "behøver":
1) være nødsaget til at gøre noget bestemt (fordi det er nødvendigt eller påkrævet) =be compelled to do something specific (because it is necessary or required)
1.a) handle eller føle på en bestemt måde eller være i en bestemt situation fordi der er grund til det =act or feel in a specific manner or be in a specific situation because there is reason for it
2) have brug for noget som man dårligt kan undvære; nødvendigvis måtte have =have a need for something it is difficult to do without; necessarily must have
2.a) kræve; have brug for; stille krav om =demand; have need of; claim for
3) bruges for at udtrykke generel nødvendighed eller behov i en bestemt situation =used to express a general necessity or need in a specific situation
3.a) bruges for at udtrykke at noget nødvendigvis skal være eller forholde sig på en bestemt måde =used to express that something necessarily have to be or take a specific position (opinion) [If anyone have a better translation of "forholde sig på en bestemt måde" feel free to comment.]
3.b) bruges for at udtrykke at noget (blot) kræver en bestemt handling fra en person for at kunne ske =used to express that something (just) requires a specific action from a person to be able to happen
Clear as mud? Well I hope it was of some use. If you would like me to try to clarify further or translate more of the dictionary page please let me know.
"Behøve" might be fairly rare, but it is definitely used sometimes.
Personally it would be very natural for me to say a sentence like "Bare fordi man har travlt, behøver man ikke være uhøflig" (Just because you are busy, doesn't mean you have to be rude). There is no real way you could rephrase that sentence with "bruge".