Java is totally viable for nearly anything; it just doesn't work well for games because they require low-level access to graphics hardware (which is definitely not something Java supports).

Also, the state of the JVM on the desktop is kind of sad - also from the graphics perspective. But Java is probably the most performant server-side language out there at this point (if you exempt the masochists who write network code in C/C++).

Java isn't viable for anything that requires low latencies and predictable throughput. Really, no GC language is.

There are companies using Java for HFT now as well.

I'm actually working for such a company. Peter Lawrey is a renowned advocate for efficient use of java in HFT.