My Norfolk Island pine is not doing so well; the needles are turning brown and the branches are drooping.
Why did this happen to my plant, and how can I cure it?
Click photos for full size
My (limited) understanding of Norfolk Pines is that they:
Are the branches drying out - it looks that way in the picture to me.
Did you recently re-pot it?
Are you perhaps over- or under-watering it it? We usually water our indoor plants once the top inch has dried and then water them until we see some water in the bottom tray.
What about fertilizer? There are indoor plant fertilizers and this plant might benefit from that if you aren't already giving it an occasional does of an appropriate fertilizer.
One thing about this tree that I read is that it really does best when it gets direct sunlight and enough moisture. The humidity level in most houses is going to be much lower than what the Norfolk Island Pine will want and so misting it often with a spray bottle will help. A humidifier would help too, though that is a bit more of an investment.
From here the Norfolk Island Pine likes
My experiences with this plant is that the dry conditions (relative humidity less than 40%) that are so common inside our houses are not ideal for this plant. Under less than ideal conditions it will drop lower branches as fast as it grows new ones from the top.
A south exposure is too hot in most locales and bright northern light is better in the Western hemisphere.
Wikipedia notes that
I do not agree that these plants need saline air but suspect that a sandy soil with constant access to moisture would be more successful than the common peat based soil and regular waterings. A wicking system as described in the link would be a low maintenance alternative.