As of Minecraft 1.3.1, which brought about server commands, weather is able to be toggled on and off via the following conmmand:
toggledownfall | Toggles rain and snow.
To run commands (by enabling cheat mode upon map creation):
Commands being entered into the Minecraft client itself must be
prefixed by a slash (example: /me flips a table). The command window
is identical to the chat window and can be accessed by pressing T or
starting directly by entering a slash. Commands being executed via the
console are not preceded by a slash.
Otherwise, if you do not have cheats enabled, you can sleep in beds (only at night!) to skip weather.
Also, if you're playing on survival, and you have the perfect opportunity for a screenshot, but no cheats mode, a quick tip is to "Open to LAN" your game (hit esc, click open to LAN), and enable "Cheats Mode: ON".
Then, toggle the weather off, and screenshot away!