Jayster
https://jayster.bandcamp.com/
Serving as the inspiration for this piece, I found out about Jayster most recently. His style is heavily 8-bit, and his remixes don't stray far from the classic NES and SNES roots of gaming music. If it's chill background or study music you're looking for, look no further.
https://joshuamorse.bandcamp.com/
As mentioned in part 3 of my Mega May coverage, Joshua Morse is at the top of my list when it comes to video game remix artists. More than simple 8-bit midi beats, Joshua Morse injects all of the songs he remixes with a heavy dose of his own flair, covering everything from Final Fantasy to Castlevania, Sonic the Hedgehog, Mega Man, Street Fighter, and even Sim City. His newest album, Arcade Attack, was released in April, and is a must-listen for fans of Sega Genesis and Super Nintendo.
DJ Cutman
http://music.djcutman.com/
Taking his name (and costume when he performs) straight out of Mega Man, DJ Cutman pumps out some head-bobbing jams by remixing them with thumping bass, for a much more techno/house music feel. Don't worry, his music spans no shortage of games and systems, not just Mega Man as his name implies.
Anamanaguchi
http://www.anamanaguchi.com/
Most known for creating the entire soundtrack for the Scott Pilgrim video game, Anamanaguchi creates all original music, but in a chiptune style that's hard not to love. Even if it isn't straight up video game music, you can't help but hearken back to the glory days of the NES when you hear their upbeat jams.
Starbomb
iTunes, Amazon
Game Grumps hosts Arin and Dan, along with Dan's band mate Ninja Brian, form the comedy group Starbomb. Their music as a feel similar to other comedy rap groups like The Lonely Island, and is definitely not for kids. That said, it's always good for a laugh, and no games or characters are safe.
SmoothMcgroove
https://smoothmcgroove.bandcamp.com/
Have you ever wanted to hear your favorite video game song sung acapella by the same guy in nine different harmonies? Well then look no further, SmoothMcgroove has got your back.
The Warp Zone
iTunes, Amazon
These guys aren't necessarily straight up musicians, but YouTube comedy channel The Warp Zone has plenty of jams from a wide variety of games. Whether it be Weird Al-style parodies of existing songs, or their catchy "Unplugged" versions of classic game music, they've got something for everyone.
Not all of this music is available through conventional means like iTunes, Amazon, and Google Play. But worry not! I've got you covered.
Gamechops.com functions as a label of sorts for video game remix artists. Joshua Morse and DJ Cutman are among their artists, and one of my favorite (and most played) albums, the all Sonic the Hedgehog "Spindash," came from this site.
If you're looking for the official soundtracks to your most beloved games, Sumthing.com is the place to go. This site has an absurd amount of game soundtracks pulled straight from the source. These aren't remixed or 8-bitted, but if you want the official song you remember so dearly, here's the place to look. Personally, I've nabbed the Devil May Cry OST from this site, which comes in two volumes, and contains every scrap of music from DMC 1-4.
Not every artist is lucky enough to make it to the bigtime. Those who don't, but still want to share their music choose BandCamp.com. This pay-what-you-want site is bustling with chiptune and remix artists. Joshua Morse, Jayster, DJ Cutman, and so many more can be found here.
The best part of sites like BandCamp, YouTube, and even iTunes is that their libraries are always growing, and there's no way to hear it all. So I want to hear your suggestions! What artists do you love that I missed? No, seriously...I need more. MOOOOORE!!