Operator overloading in C++ is considered by many to be A Bad Thing(tm), and a mistake not to be repeated in newer languages. Certainly, it was one feature specifically drop
Operator overloading is not something that you really "need" very often, but when using Java, if you hit a point where you genuinely need it, it'll make you want to rip your fingernails out just so you have an excuse to stop typing.
That code which you've just found overflows a long? Yup, you're going to have to retype the whole lot to make it work with BigInteger. There is nothing more frustrating that having to reinvent the wheel just to change the type of a variable.
As the other answers have pointed out; operator overloading itself isn't necessarily bad. What is bad it when it is used in ways that make the resulting code un-obvious. Generally when using them you need to make them do the least surprising thing (having operator+ do division would cause trouble for a rational class's usage) or as Scott Meyers says:
Clients already know how types like int behave, so you should strive to have your types behave in the same way whenever reasonable... When in doubt, do as the ints do. (From Effective C++ 3rd Edition item 18)
Now some people have taken operator overloading to the extreme with things like boost::spirit. At this level you have no idea how it is implemented but it makes an interesting syntax to get what you want done. I'm not sure if this is good or bad. It seems nice, but I haven't used it.