I ran into this issue recently and resolved after trying several solution others suggested. I will give you my solution first and then list the other things I tried since every one will have a different environment. This solutions applies for WordPress on GoDaddy hosting.
The problem, when trying to upload media to post or anything, I got this error
Unable to create directory /wp-content/uploads/2009/01. Is its parent directory writable by the server?
The solution that worked for me was to simply update the path of the media upload directory in WordPress (Settings / Media) to “wp-content/uploads” or leave it blank to force default. For some reason this field had something like /home/”some other stuff”/wp-content/uploads. After making this change I was able to upload with no problem.
Other possible solutions (these did not work for me but it will be good the check)