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 mode 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!