You need the JAI ImageIO package:
http://java.net/projects/jai-imageio/ (Note that this is different from JAI itself, which is not needed.)
In theory, ImageIO should pick up TIFF support automatically if you have it in the classpath, but I haven't gotten that to work. So you may need to register it in code:
That's all there is to it. The library also contains a GIF writer (which JDKs < 1.6 don't have), as well as RAW, PNM and JPEG2000 readers and writer, just in case you ever need those.