I should start by saying that I have absolutely no affiliation to Apple or any of the apps their products run.
I found this app a few months ago, and I can't live without it: Storm Sim (running on my ipad mini and Iphone 4)
Call me lame, but I love the sound of rain and thunder when I'm trying to work, relax, or sleep.
The free version is great, but the paid version (which is like... 2 GBP or less) is even greater.
You have a library of different sounds (different levels/types of rain, animals, and a limitless list of thunder sounds)
The best part is that it never ever ever sounds like you've got a Youtube video on repeat. I've listened to it for hours and hours on end and never felt like it was fake and repetitive.
You can create your own storms, use their default ones, and edit their default ones.
You can use it as an alarm clock: it'll ask you what time you want the storm to start (which will gently fade in so it doesn't wake you up with a startle), and what time you want it to soothingly awaken you from your slumber (slightly louder, and stormier).
On the reverse, you can put it on with a countdown timer to help you sleep, gently fading out so it doesn't wake you up just as you've dosed off.
I genuinely cannot quite explain just how amazing this app is.
Here's a screenshot I found on Google: http://www.lostintechnology.com/wp-content/uploads/2011/09/storm-sim-free.jpg
Try it. I swear to all things beautiful that you'll love it (if that's what you're into).
EDIT following comment:
Developer: Obsolete Software (www.obsolete-software.com)