I believe you can upload videos to dropbox (i have, though that was over a year ago). Back then, it would only upload over WiFi though. Don't know if either of these facts have changed since then.
Also, I have a Google plus account, and my videos also upload there automatically (also over wifi) - although I've seen some people on this forum have had issues with uploading videos to Google plus in the past. Not sure what current status is on that.