There's nothing wrong with recursive algorithms per se. They tend to be shorter, and look more elegant when implemented, although that can be deceiving.
One example are the Fibonacci numbers. They are usually defined recursively, and very easy to implement that way. But the recursive approach has exponential complexity, while it's easy to implement an iterative approach that has linear complexity.
So the answer is, it depends. They're neither always faster, nor always slower, than comparable non-recursive algorithms. I'm mentioning this because I've seen both opinions stated numerous times, and they're simply not true. [ February 20, 2008: Message edited by: Ulf Dittmer ]
The problem with recursion is that it can be hungry on memory; I find on my PC that recursions which get out of hand cause a StackOverflowError somewhere between 3000 and 4000 calls. But recursion done correctly is a nice technique, as Ulf has told us.
But I know how to write a Fibonacci recursion which runs in linear time, and if you look in Anne Kaldewaij's book Programming : the derivation of algorithms Hemel Hempstead : Prentice Hall International, 1990, I think page 98, you can find how to write a Fibonacci number which runs in logarithmic time.
The alternative to recursion is iteration, which in Java means while, do-while or for.