The main link isn't bad but I prefer on-location videos - I look for actual field recordings (not loops off some sound effects CD), in stereo if possible, and I prefer percussive sounds as I find them more relaxing. YMMV. I also like to see the rain.

JWWargo's post: http://sensibleendowment.com/entry.php/11729

One of the first I found was this one, under an umbrella:
https://www.youtube.com/watch?v=IFGS_NVsYGk

This was shot in Norway and for some reason I find both sound and picture very soothing (probably means I'm a white supremacist death metal fan at heart):
https://www.youtube.com/watch?v=dWoIljGEOQ4

I love driving in the rain, and so does this guy, who has a bunch of these:
https://www.youtube.com/watch?v=-WdtGcBUkb0
https://www.youtube.com/watch?v=cS3B8gM0YYk
https://www.youtube.com/watch?v=0m88GfmICBQ
Parked: https://www.youtube.com/watch?v=7GhIWi_zybw
Parked: https://www.youtube.com/watch?v=LPs5hxAz_E0
Carport rather than car: https://www.youtube.com/watch?v=-WdtGcBUkb0
In a tent: https://www.youtube.com/watch?v=WSlgKZrHJg8

His YouTube channel is here:
https://www.youtube.com/channel/UCt8qFyujmbUj15bAveVhdCw

Under a poncho, good spatialization:
https://www.youtube.com/watch?v=k4a9kxtvMbU

Rain on a tarp:
https://www.youtube.com/watch?v=0AE_DeeW9bw

Rain on car roof:
https://www.youtube.com/watch?v=guo8CHurCpY

My current favorite, rain on a campervan roof (also in Norway, hmm...):
https://www.youtube.com/watch?v=Xd2NYsuU-zs

Watch out for the ads, when I find one I like I often use a site like en.savefrom.net to download the video and save it.

I have a bit of ASMR:
https://en.wikipedia.org/wiki/Autonomous_sensory_meridian_response

...which I think is part of the reason why I like percussive stereo rain. If you respond to it ASMR videos can be great for falling asleep. You can search YouTube for "ASMR" to find more conventional examples (most of them involve young women pretending to brush the viewer's hair or give them a massage while speaking in a soft voice - and many of them seem to be blonde, look, there I go again.)

Here's an ASMR video with rain on an umbrella:
https://www.youtube.com/watch?v=dScslgkAHJU

Here's one with talking and rain sounds (but they may be fake):
https://www.youtube.com/watch?v=dT4HaS40Mnk

I also use apps sometimes to help me sleep. Some of my favorites are:
iSleep Easy and
Rain Rain (this one's very customizable)

These are on iPhone but I think are on Android as well.