1. Eclipse 3.7(Indigo release) will not be shipped with Java 7 support. This is not because we folks at JDT are lazy and didn't want to do the whole work by the time 3.7 is wrapped up (Well, it might be true sometimes, but then we have tough taskmasters as well!!). This is mostly because the official release of Java 7 is scheduled on July 28, 2011, and we'd have already wrapped up 3.7 before that. The delay, in part, has also been caused due to the late availability of JSR-292 (Invoke Dynamic) and JSR-334 (Project Coin).
2. Eclipse folks are busy working overtime to make sure that Java 7 support is in place by the time we ship Eclipse 3.7.1. As per bug bug 288548- "The work for the Java 7 features is currently in progress in the 'BETA_JAVA7' branch and we will deliver separate updates for the stable builds in order to provide early access to the Java 7 features for interested parties."
3. Much of the compiler support is already in place, and some work needs to be done on the UI portion. To check the progress on BETA_JAVA7 branch, you can read through JDT Core java 7 wiki page.
4. If you want to test Eclipse's java 7 support, or want to use Eclipse to try out the new java 7 stuff, you can follow the instructions given in the "What to do to set up the IDE" section of the JDT Core java 7 wiki page. We plan to have downloadable builds soon. You can see the list of open bugs against JDT/Core Java 7 support at any point in time here. To report new bugs, make sure you use the [1.7] tag.
Hope this helps!