I had the same problem. I had just uploaded a site which I developed locally using XAMMP. Everything was final locally, and it looked fine once I had uploaded it to my GoDaddy hosting (whih hosts other WP sites, all working fine).
Then I noticed I couldn’t upload media to the hosted site. Checked all the folder permissions against another of my site which was working fine, and all the content folders were 705.
Then I noticed the post about the ‘Store uploads in this folder’ setting. So I checked my Misc settings and found it was set to ‘/wp-content/uploads’. I changed it to ‘wp-content/uploads’ (i.e., no leading slash) and presto, now I can upload media!
