Tutorials:
It's linked in the above list, but just to have it standalone: http://pixeljoint.com/forum/forum_posts.asp?TID=11299 (I consider it THE intro pixel art.)
Post by FrankenGraphics and Myself about Pixel art: http://forums.nesdev.com/viewtopic.php?f=21&t=16999 (My post starts out a bit ranty, I guess. But the end piece of it does analysis of NES background art.)
Tools:
I-Chr: https://kasumi.itch.io/ichr (Disclaimer: I wrote it.
I genuinely believe it's actually one of the easier ways out there to see graphics you made in a ROM, tools-wise.
It also has a forum topic here if you have questions.)
NES Screen Tool: https://shiru.untergrund.net/software.shtml (Simple art program that will force NES restrictions on you.)
NiGo-CHR: https://retrodaddy.itch.io/nigo-chr (Not the most user friendly program, but it's built from the ground up for NES and has some pretty advanced features.)
Misc:
VGMaps: http://www.vgmaps.com/Atlas/NES/index.htm (Ripped maps of LOTS of NES games. Useful for study. I recommend checking out RoboCop3, Mighty Final Fight, and Star Trek as far as games on there that aren't super famous, but still have good graphics.)
Detailed post I wrote on NES graphical restrictions: https://pixelation.org/index.php?topic=10784.msg115062#msg115062
Shorter infographic I made:
FrankenGraphics' Blog: https://frankengraphics.com/ (Not quite tutorials, but some good thoughts on NES graphics design.)
M-Tee's Blog: http://www.mteegfx.com/ (Not quite tutorials, but some good thoughts on NES graphics design. Some of the meaty info is pretty far back in the blog.)
surt's Open Game Art Gallery: https://opengameart.org/users/surt (He allows some of his work to be used freely, so you can use his awesome art for your own games! Make sure to carefully read the terms of each set you use, though!)
surt's Gallery: http://pixeljoint.com/p/2254.htm (Does a lot of retro pixel art, some of which is NES restrictions.)
Ptoing's Gallery: http://pixeljoint.com/p/2191.htm (Does a lot of retro pixel art, some of which is NES restrictions.)
ryumaru's Gallery: http://pixeljoint.com/p/3304.htm (Does a lot of retro pixel art, though more Game Boy focused than NES.)