You can upload replays to Mario Kart 8's Mario Kart TV mode to a site where others can watch and share your videos. That site is called mariokart.tv, and it's up right now.
Hitting the site lets you watch the most recent videos uploaded by players, but logging into the system with your own account lets you watch your own videos. From there, you can link out to social networks if you'd like. Oh, and it works nicely on a mobile phone, too.
I'm glad I didn't save any replays from my matches against my friend from this past weekend. You've never seen someone fly off track so much.