Most of the songs I like are at least somewhat obscure. Some of them are very obscure. Others are by the Beatles.
There is a type of music I am rather fond of that I call "unmusical music". The more musical end of this seems to be called "minimal wave". The less musical end is known as "harsh noise". I suppose "power electronics" is somewhere inbetween.
I'm not sure if most people view these as similar in the way that I do, but to me, all of these have the commonality of feeling like the musical equivalent of a mental breakdown. They make me feel like I'm being pinned down or like I'm a kitten being held by the scruff, and I mean this in a good way. This music is relaxing in a very deep way. The times I've been the most actively distressed, I feel extremely exhausted afterwards. These types of music basically skip to the extreme exhaustion without the distress required, and somehow that just feels calming.
Oh, and also it sounds good.
Another type of music I'm fond of are "Beatles Outfakes". That is, songs that have been misattributed to the Beatles. Some of them don't really sound like the Beatles. At all.
Anyway, here's some lists of songs I particularly like: