Since 2011, Stack Exchange use Imgur to handle pictures. If I personally have no problem with Imgur so far, some workplaces can have. Mine for example... Why a company would block it? Imgur is an online image sharing community and can be see as a complete social network like facebook, tumblr or twitter. Also, you can easily find NSFW content on Imgur...
I am not sure what could be a solution. Proxy, VPN, or else can be strictly forbidden. Two ideas:
Use another DNS from Imgur
See with Imgur to use another url. For example,
http://i.stack.imgur.com/VB5JX.png could be
http://i.stack.imgurpro.com/VB5JX.png. This move the problem to the side of Imgur.
Switch from Imgur to another solution
It could be self-hosted or another more "professional" hoster. I am sure that if you come to use Imgur that because they offers a lot of benefits. So not really a solution...
I welcome any other ideas.