It's all a question of context. Some people have already given examples where static is absolutely preferable, such as when writing utility functions with no conceivable state. For example, if you are writing a collection of different sort algorithms to be used on arrays, making your method anything but static just confuses the situation. Any programmer reading your code would have to ask, why did you NOT make it static, and would have to look to see if you are doing something stateful to the object.
public class Sorting {
public static void quiksort(int [] array) {}
public static void heapsort(int[] array) { }
}
Having said that, there are many people who write code of some kind, and insist that they have some special one-off code, only to find later that it isn't so. For example, you want to calculate statistics on a variable. So you write:
public class Stats {
public static void printStats(float[] data) { }
}
The first element of bad design here is that the programmer intends to just print out the results, rather than generically use them. Embedding I/O in computation is terrible for reuse. However, the next problem is that this general purpose routine should be computing max, min, mean, variance, etc. and storing it somewhere. Where? In the state of an object. If it were really a one-off, you could make it static, but of course, you are going to find that you want to compute the mean of two different things, and then it's awfully nice if you can just instantiate the object multiple times.
public class Stats {
private double min,max,mean,var;
public void compute(float data[]) { ... }
public double getMin() { return min; }
public double
}
The knee jerk reaction against static is often the reaction of programmers to the stupidity of doing this sort of thing statically, since it's easier to just say never do that than actually explain which cases are ok, and which are stupid.
Note that in this case, I am actually using the object as a kind of special-purpose pass by reference, because Java is so obnoxious in that regard. In C++, this sort of thing could have been a function, with whatever state passed as references. But even in C++, the same rules apply, it's just that Java forces us to use objects more because of the lack of pass by reference.
As far as performance goes, the biggest performance increase of switching from a regular method is actually avoiding the dynamic polymorphic check which is the default in java, and which in C++ is specified manually with virtual.
When I tried last there was a 3:1 advantage of calling a final method over a regular method, but no discernible for calling static functions over final.
Note that if you call one method from another, the JIT is often smart enough to inline the code, in which case there is no call at all, which is why making any statement about exactly how much you save is extremely dangerous. All you can say is that when the compiler has to call a function, it can't hurt if it can call one like static or final which requires less computation.