Look for Patterns & Reflections
Rain brings out some interesting patterns which are an important aspect of photography. Patterns can make your composition almost irresistible. If you look around carefully enough you'll notice several patterns that come up during rain and serve as wonderful objects for abstract and architectural photography.
As the picture on the right shows, even a simple spider web with water droplets can make up a very interesting composition. Another great rainy day photo is rain droplets acting as mirrors producing a plethora of reflections. This kind of an image is difficult to come across, but if your look for it you'll definitely find it. Try shooting with a shallow depth of field so that the water droplets and their reflections are in perfect focus, remember that you're trying depict pictures inside a picture!
Once you get the hang of it, you'll start churning out photos like this, with great compositional value, frequently. Its like swimming, its difficult when you learn it, but once you've trained yourself the eyes never miss the scenes.
Another interesting aspect of shooting under rainy conditions are reflections! Rain water serves as light reflectors, depending on how you compose your shot. I recommend starting with trying to take photos of reflections in the water, once you get a hold of this you can move onto to more advanced tricks. Reflections add a sense of awe, as well as an abstract feeling, to your photographs. So, remember to scan each and every puddle that you come across for that great view that you would never come across on a bright and dry sunny day.