I am a Java developer by profession, so yes, I like it. Wouldn't be doing it otherwise :-D
Creating a program in Java usually means it'll be pretty easy to get it running on Windows, Linux and Mac (although some issues might require more thinking through because of differences in the way those systems work).
If you want to go mobile, Write-Once-Run-Anywhere doesn't apply anymore. Every device and every manufacturer seems to support a different set of API's and profiles. Blackberry has it's own graphics API for example (no AWT), while others do depend on AWT but have different implementation bugs. That's what Amiga-Anywhere tried to fix (and it worked quite well) and it's also what Google Android tries to fix. Android, again, uses their own custom API's but they hope to cover a huge number of mobile devices with their platform.
Sun has recently been paying a lot of attention to a better user-experience, which is especially important if you want your program to work in a webbrowser. Soon those updates will be released, but you can already download
update N.
Writing games is also perfectly possible, but usually you'll end up using native libraries for hardware accelleration and those libraries don't always work inside a browser (Java applets). For writing games I'd advise you to take a look at
Slick.
My favorite browser is also
IntelliJ IDEA, but if you're just getting started, one of the Open Source IDE will probably do just fine for you. Or maybe just
JCreator. It's a great high-performance IDE with less bells and whistles, so it'll be easier to get started (less stuff to work through). They offer a light-edition for free, but it'll only work on Windows.