Prediction is not necessarily prediction; it might actually be inferences or even observations.
As oshirowanen mentioned, there are two kinds of predictions: Magical Prediction and Scientific Prediction.
(Actually I don't believe them as prediction)
The term "Scientific prediction" is a misnomer .The correct terms are Scientific Inference, Statistical Inference, Computation or Calculation. None of which predict unseen in the literal sense, but do give a rough estimate given historical data.
Weather forecasting and similar predictions fall into this category. They're usually statistical and probabilistic approaches. So like any other helpful science they are not haram (And Allah knows best).
As Wikipedia states, they are definitely haram . The evidence for this is found in the following ayah:
They followed what the evil ones gave out (falsely) against the power of Solomon: the blasphemers were, not Solomon, but the evil ones, teaching men magic, and such things as came down at Babylon to the angels Harut and Marut. But neither of these taught anyone (such things) without saying: "We are only for trial; so do not blaspheme." They learned from them the means to sow discord between man and wife. But they could not thus harm anyone except by Allah's permission. And they learned what harmed them, not what profited them. And they knew that the buyers of (magic) would have no share in the happiness of the Hereafter. And vile was the price for which they did sell their souls, if they but knew!
However, some of the prophets were able and allowed to predict the unseen future with the permission and help of Allah (of course again not magically, the knowledge was directly from Allah), as evidenced by the following ayat:
عَالِمُ الْغَيْبِ فَلَا يُظْهِرُ عَلَىٰ غَيْبِهِ أَحَدًا
[He is] Knower of the unseen, and He does not disclose His [knowledge of the] unseen to anyone
إِلَّا مَنِ ارْتَضَىٰ مِن رَّسُولٍ فَإِنَّهُ يَسْلُكُ مِن بَيْنِ يَدَيْهِ وَمِنْ خَلْفِهِ رَصَدًا
Except whom He has approved of messengers, and indeed, He sends before each messenger and behind him observers