As of this writing, the SGI version is expected to release by the end of April, along with a new version of Cosmo Code that supports it. That's the good news. For people writing Java applications there isn't any. Feel free to start writing code that takes advantage of the new features. Of course, you'll need to make sure that all of your users are running the 1.1 version of the JVM before you can take advantage of any of the new features.
Applets are a somewhat messier story.
We can expect both Netscape and Microsoft to release versions of their web browsers that support the new JVM before very long. How long it will take for the majority of users to upgrade is, as always, harder to predict. If you are concerned about having the widest possible acceptance of your applet you'll need to stay away from the wonderful new features of JDK 1.1. Fortunately, Java does a good job of both upward and downward compatibility. Stay within the limits of what was available with JDK 1.0 and your code built with 1.1 will be usable by everyone.