Most of my site images are on the same server the files / database are, so it wouldn't affect me too much. I use TinyPic for quick uploading though, so only them closing would really tick me off. Of course there are many others to turn to;
I rarely use any image site hosts but if it was down I'd go to the millions of other image hosts. Like when a forum goes down, there's billions of others I could go and post, etc on.
I would just use another image host,
When I upload a Image to tinypic I save it to my computer,
I had my forum banners hosted with a huge upload site and had them advertised on many sites and the site just removed them, So I had to upload them to tiny pic,
I use Photobucket, not tinypic. I was asking myself the same question last week, what if photobucket went down? All of my photoshop portfolio is uploaded on there, and since I moved to a new laptop, I no longer have a different copy of them. Considering that PB was acting up for me that night I ended up making a second copy on my laptop, took me 2 hours organising everything 😛