Hehe, I wrote the same thing for the railway simulator Trainz about 5 years ago now.
Sprites are the way to go, because you don't need more than a couple dozen of them hitting the screen at once to get a realistic effect.
I simply took the resolution of the screen that the user was running the game in, took a random position from that width and height, and placed a nice semi-transparent blob of rain on the screen, making it slide down the screen and fade out as it went.
The timing between each initial creation is up to you (can't remember exactly how I decided to do it, but it was probably every half second), and once you have your maximum number of raindrops, just keep checking the number of objects every half second, and create a new one every time the number drops below your maximum.
The old drops are destroyed when they've completely faded out, which makes room for each new one to be created.