How can I write a GEOTIFF in Java?

GeoTIFF-JAI should be able to do this:

http://sourceforge.net/projects/geotiff-jai/

GeoTIFF-AI incorporates Extensible-TIFF-JAI, which is an extensible codec allowing tiled images, etc.

There's also a GeoTIFF metadata adapter for Java ImageIO at:

www.gelbin.org/code/

and the NetCDF library also includes a GeoTIFF writer, documented at:

www.unidata.ucar.edu/software/netcdf-java/v4.0/javadocAll/ucar/nc2/geotiff/GeotiffWriter.html