Unless it's a low snow year, or you have the skills and gear to navigate on snow and traverse steep and slippery snow slopes, much of June will be too early for most of the Colorado Trail. There are some lower sections such as the Lost Creek area (check with our Colorado folks here). The same is true for most of the PCT and CDT, at least the interesting parts. Again, a lot depends on the snow pack. In the Cascades and Sierra, it's dangerously low. Of course there have been other years (actually, the last two) in which winter didn't really start until March! Here is a good place to keep track of the general snow depth. Since June is an iffy month for the western mountains, you might want to have at least a Plan B in mind. That's an especially good idea for the drought-stricken areas--the snow may be gone but the fire danger will be extremely high. (I learned that lesson five years ago!)

There are lower elevation possibilities: The Olympic National Park wilderness coast is one (lots of info on the Olympic NP website). California's Lost Coast is another. Remember that the eastern US has mountains, too, some (like New Hampshire's Whites) quite spectacular, and they'll be available (although buggy) in June!

BrianLe, I just read that the Gila River flooded last fall and is a real mess. People on the CDT-L are questioning if it will even be open this year.