Are raindrops actually "shaped like tears" when they fall? Raindrops are always pictured like this, people imagine they have this shape when they fall, but is this true? Doesn't this shape create too much drag? What shape do they really have? It would also be nice to know how is the actual shape formed regarding the flow of air. 

 A: They can sometimes have this shape as they stretch downward from a faucet, as seen in this video, however, surface tension usually pulls the droplet into a roughly-spherical package. The reasons that raindrops have "streaky" trajectories in photographs is not that the raindrops are distended by air resistance, but rather that the short exposure time of the camera is still long enough that the raindrop moves a surprisingly large distance in that small time, and each point that it appears gets partially exposed. 
As they hit terminal velocity the force against the bottom is large enough that they have to have a cross-section which looks a little more like a "bean": the side facing "downward" gets flattened by the wind resistance and eventually the center can even be pushed upwards into the droplet; the trailing edge retains its "bulge" upwards. See e.g. this video.
A: The diagrammatic representation of rain is indeed incorrect. Raindrops do not resemble teardrops. 
This Youtube video by Minute Physics provides a really cool explaination of that: http://youtu.be/8lBvC7aFB40
A: Indeed, they have shape of oblate spheroids -i.e., spheres squashed along the fall axis. E.g., this article says

Falling raindrops adopt a range of shapes depending on their size—though never the teardrop shape in-
scribed in the public imagination (Blanchard,2004). As raindrops grow in mass, they evolve from spheres to
oblate spheroids to shapes resembling the top of a hamburger bun (e.g., Beard & Chuang,1987; Pruppacher
& Pitter,1971). (An oblate spheroid is generated from an ellipse rotated about its minor axis.)

The quoted article contains a section on the raindrop shapes and uses this shape to calculate the air resistance and the drop terminal velocity. One can learn more from the books cited.
