Imgur is a totally separate entity, the company was founded by Alan Schaaf using reddit as a place to "launch" it[3], they've never announced outside funding and there has never been any talk of reddit (or Advance Publications, or Conde Nast) having any ownership stake.[4]
[1] http://www.reddit.com/r/TheoryOfReddit/comments/14unl6/reddi...
[2] http://www.reddit.com/r/lounge/comments/1g73ec/whats_reddits... (screenshot: http://i.imgur.com/ZoQKmOh.png)
[3] http://www.reddit.com/r/reddit.com/comments/7zlyd/my_gift_to...
imgur was the first image host (before minus) that didn't suck, wasn't anti-user, freely allowed hotlinking and had a minimal page when they didn't hotlink.
It's almost never down and the links don't magically fail or expire after they get lots of traffic like many other hosts.