These aren't remixes or dubstep or electronic, but I'm a supporter of broadening musical horizons so here are 3 songs of various genres.
Pinch Me - Barenaked Ladies
A pretty happy-sounding song with an actually quite dark meaning if you look into the lyrics.
Where is the Heart - Alex Clare
I really like the beat to this one. Alex Clare has made some pretty good songs, a notably popular one being too close ("And maybe I am just to close to love you! etc.")
I'm Impressed - They Might Be Giants
A strange band with a strange name. They're not for everyone, but I really love their catchy songs and crazy lyrics mixed with a really unique sound.
Bonus Round! Japanese Music!
So I'm (attempting) to learn Japanese and am really interested in their culture. I've started to really like some Japanese musicians, some of whom I've discovered through Anime openings.
Suna no Oshira - Kanon Wakeshima
While I didn't discover her through her compositions for the anime Vampire Knight, I love her use of cello and dark sound to her music.
Omakage Warp - nano.RIPE
Discovered the band through their OP/EDs for Hanasaku Iroha. Love the unique voice of their lead singer, and the nice alternative rock sound.
Imagination Forest - Jin
https://www.youtube.com/watch?v=lfq7T0H6cCI&index=42&list=PLw4C13Qobqyc4-0Wm_4OCVdNxHJIRiP2n
I had to put video url because apparently you can't link to more than 5 videos per post.
A vocaloid song (vocaloids are artificial singers basically, where the voice is created using software), from a series of them that tell the story of the Mekakushi Dan. It's highly regarded as one of the best of it's kind, and I highly recommend watching the lyric video for it, as the story it tells is quite good. There's playlists out there that compile all the songs with lyrics in chronological order. Just google 'Kagerou Project' for more info.
If you want more recommendations, be sure to tell me! You can also view my full playlist of favorite songs here:
https://www.youtube.com/playlist?list=PLw4C13Qobqyc4-0Wm_4OCVdNxHJIRiP2n