OK, I don't mean to be a sourpuss or anything, but does the fact that I have never heard of 95% of the bands people are listing mean that I am hopelessly out of touch, or that people around this forum tend to gravitate (deliberately?) to obscure acts?
Um, I'm pretty sure you're out of touch. Not because you haven't heard of these bands specifically, but because you aren't aware of that being a "normal" occurrence now-a-days. There's just too much awesome music out there to keep up with. My band members and I are all really into current music, but when we get together we still spend a lot of time just introducing each other to new bands... and we all have similar tastes!
I do have to say though that I HAVE recognized most of the bands listed so far, and the large majority of them are fairly popular groups... not Lady Gaga or Nickelback popular, but definitely "indie" popular.
So, anyhow, on to my own answer to the OP:
I mostly like "quirky" music, if it's not a bit off kilter by a few degrees I rarely have much interest in it. Terms like progressive, jazz, post (whatever), etc are pretty much where I live.
First, I would like to +1
Tera Melos, they are the quintessential "Math Rock" band in my opinion. For those who don't know, "math rock" is basically the new evolution of "Prog." It doesn't sound like 70s prog, but it has the same mindset. It takes popular sounds and ideas from modern music and combines them with more obscure sounds and ideas, "strange" time signatures, complex arrangements, and a high level of musicianship.
Tera Melos - 40 Rods to the Hogs Head
Next on my list would be
The Bad Plus. They're sort of an "indie"/jazz hybrid that takes a lot of my favorite things from both genres and manages to combine them in subtle ways that I think would please fans of either genre.
The Bad Plus - Prehensile Dream
A bit of a left turn here, but my next suggestion is
Bon Iver, soft and under stated this guy is more from the Nick Drake school of musicianship. Beautiful lilting melodies, but not without an undercurrent of depth and brooding.
Bon Iver - Skinny Love
The Dirty Projectors really sort of hit me where I live when I first heard them. I think they are, no question, the spiritual predecessors of the 70s New York post-punk scene. They wear their Talking Heads influence on their sleeves, even though I wouldn't necessarily say they sound a whole lot like TH... and yes, I know that's a contradiction, but listen to it and I think you'll agree with me
Dirty Projectors - No Intention
Finally, the first time I heard
Earthless I was shocked that anyone was still doing this sort of oldschool hendrix-style guitar noodlies over bass and drum grooves things... especially in a way that sounds so GD
relevant. Technically they've been playing for a decade now, but I think they still belong here based on the spirit of the discussion even if the OP asked for 5-6 year old bands.
Earthless - Sonic Prayer
Honestly, I could do this for days so I'm just gonna stop here for now. However, if anyone finds my choices interesting and would like me to continue pulling you guys down the rabbit hole that I inhabit just ask and I'll contribute a Part 2 to my list.