Think of static variables as class-wide global variables or, if you use "final" keyword, as class-wide global constants. Use static non-final variables wisely - they are shared among all class instances and it may lead to some non-obvious mistakes. I would recomend avoid using mutable static variables at all - there are small to none cases, where such need couldn't be implemented using dependency injection.
Also using globals always makes unit-testing lot harder - one more drawback to consider.