Because of its southern desert location, just about any time is a good time to visit Zion, with Winter being the least enjoyable (but also the least crowded).
Flowers start in April and begin to fade out in June. May seems to be an excellent time to see this desert oasis in full bloom, with Columbine and Shooting-Star being the most common flowers. Cacti bloom a bit later on average...
The Summer months bring many tourists to the area, intent on wading in the cool waters of Zion's rivers and streams.
July and August are the most active months for thunderstorms as well; if you plan on hiking the narrower canyons, you might want to work around this period (although the streams are also warmer at this time...)
Early Fall is still warm, but once school starts the crowd dies down a bit. Probably not a bad time to get in some serious hiking...
Winters can get chilly, though afternoon temperatures are often reasonable.