Hm. I would have thought that Dropbox would work. Maybe there's a privacy issue?
What about Flickr (it's back)?
From a Reddit thread:
Give these a try:
https://postimage.io/ (Unlimited Bandwidth, Free to use but compresses image **Edit: Postimage has added an option to opt of image compression during upload.)
https://lensdump.com (Unlimited Bandwidth, Raw Uncompressed Image, Keeps Exif Data, More features for registered users and Free to use, 100MB max image file size)
http://cubeupload.com/ (Amazing and simple interface, Unlimited Bandwidth, Raw Uncompressed images, Free to use, 5MB max image file size)
https://flickr.com (This one is not for everyone, it is basically a service to showcase your artistic work but works as image host as well, owned by Yahoo!)
Don't use the these image hosts; Get miles away from them. :
https://tinypic.com (Old Outdated interface, No multi image upload support, Compresses image, No hotlinking)
https://imgur.com (Compresses images, biased and deletes images based on their own opinion)
https://photobucket.com (Old, Can't upload images as guest, Parent company of Tinypic, so even worse than tinypic)
https://imageshack.us (Only paid accounts have unlimited bandwidth)
Edit: Adding some cons as requested by OP. Don't have much time as I am at the office, but I think it should give an overall idea.
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