Java's future looks bright - the magical Java SE 6 Update N is just around the corner. A modularized JRE (Kernel installation mode) for quicker downloads, more Java2D acceleration, applets running in a separate thread (which means no dreaded startup freeze anymore), and lots of other funky things.
But how well do things look right now? Good question. David Brakeen (the author of Developing Games in Java) generously shared some stats from Pulp Games (by the way the 1.4 compatible PulpCore framework is open source and pretty awesome).
The size of the sample is 3653 playing sessions (single day). Since versions prior to 1.4 account only for about 2% we can thankfully ignore 'em completely. That was about time, wasn't it?
While targeting 1.6 apparently is a bit too much for a casual web game, targeting 1.5 won't be much of an issue. Using System.nanoTime() is a compelling reason to use 1.5. There are of course workarounds for System.currentTimeMillis(), but they all come with a set of drawbacks.
If you're really fond of the 1.5 language features you can still produce 1.4 compatible bytecode with Retroweaver. The timing issue can be addressed with interfaces. Just make your timing/capping thingy pluggable and use what's available. This allows you to reach those extra 9% of users without any big compromises.
1.6 doesn't offer anything that's required for games. However, performance improved a lot (up to 48% in extreme cases such as real time ray-tracing). So, do your visitors a favor and educate 'em a bit. ;)