The answer is "probably yes, you can get raindrops to magnify images of
close-by objects", but you'd have to get really really close to the
raindrop and also put the object you'd like a magnified image of very
close to the raindrop (or better yet, inside the raindrop). Raindrops
are very small, and have tiny, tiny focal lengths. Nonetheless, they do
act as converging lenses which are convex on both sides. You might not
be able to get your eyes close enough to a tiny raindrop and keep
things in focus, though.
If you put your eye farther away from the raindrop than the focal
length, or look at faraway objects, the image will actually be smaller
than looking at things directly, and will be inverted. You can try all
of this with glass converging lenses, or, if you are so inclined, try a
spherical glass paperweight, a round fishbowl, or other clear,
spherical object (there's a really nice quartz sphere in the
Smithsonian Museum in Washington, DC).
(republished on 07/29/06)