Let me tell you how I have managed to, with about 85-90% accuracy, been able to predict a large number of inorganic reactions. There are some prerequisites to do this. They are as follows:
1. The Periodic Table: You need to learn the stable oxidation states and configurations of ions. For instance, pretty much all sulphides, upon oxidation, become sulphates, because +6 is one of the most stable states of sulphur. Or, Ferrous and Ferric ions are pretty much equally stable, so much so that I like to call them toggler ions, as the switch between each other with ease.
2. Electrochemical Series: This is extremely important. It was simply amazing how much i could put into context after learning about this series. I could now understand why Iron metal produces hydrogen gas upon reacting with an acid. It will help you in countless redox reactions.
3. Solubility of compounds (in water) This will help you to predict precipitation reactions. In lower classes, we are taught these as lousy double displacement reactions, but they are actually pretty inaccurate. A ppt reaction will occur if the initial reactants are soluble, and at least one of the products is insoluble. Le-Chatelier's principle, if you will. Also, there is usually no way to predict solubility, as it is a complex interplay of hydration and lattice enthalpies, so you HAVE to memorize.
Now, a lot of reactions have no apparent logic, so there is no way to predict them. You will have to memorize these.
For instance, in the Rasching's process to prepare hydrazine, Ammonia reacts with the hypochlorite ion to produce chloramine. This cannot be predicted with the above steps. It has to be memorized.
All I can say is, inorganic chemistry needs 55% memorization, and 45% common sense, which includes some intrinsic feeling as to what should be the outcome of a reaction, which will develop after a lot of practice.