Some of these seem pretty obvious but you would be surprised at how many girls don't own a good pair of boots for the rain. There's so many different style rain boots now and they come in many colors and prints too. I got mine from ebay last year for only $25. I switch off using either my rubber boots or if the rain is not that bad, I opt for my combat ones. I just picked these 3 different styles to show you.
I lose umbrellas all the time, so I found the best way to stop doing that was to buy one of these mini umbrellas from H&M that I can just keep in my bag all the time. That way it's always with me in case it starts to rain. They have different colors & prints too. If you prefer a larger umbrella but want a different style, these bubble shape ones are really cute.
Another good way to protect your hair from the rain is going with a wide brim hat, depending on the material of course. Or you can also wrap your head in a decorative scarf as well like the one above. If it's a rainy day and I don't have anywhere special to be, I usually just throw my hair into a bun.
Trench coats are great for the rain because they're stylish and also protect you from getting wet like this one. Or if you prefer, you could also go with an actual rain coat like the one from Forever21. Not all rain coats are ugly, you just have to search for one that you like.
I wear leggings a lot in the rain and they're the simplest thing to pair with my rubber rain boots. As I mentioned I got my boots last year.. before that I never had anything to really protect my feet from the rain and I would always get soaked. Not a smart move I know.
I'm sure there's other things you could get as well but these were the first ones that came to mind. Stay dry! :)