Yes, there is a breathtaking amount of copyright infringement going on on the internet.
The thing is: where it concerns images, most of it happens with the implicit approval of the copyright holders, who basically like to have their stuff shared and pinned and retweeted all over the internet (at least by consumers) because that gets them attention and ultimately money. They don't make it official by putting the stuff under a permissive license because they want to retain the ability to stop other companies from finding ways to get that attention money instead of them. But as long as the copyright holder tolerates it, infringement can happen without consequences.
The exception are images which are themselves products, such as professional photography and art. Copyright holders do very often seek out and sue infringement in such areas. But even there, allowing low-resolution and watermarked versions to be shared is common.
On the legal and organizational level, the key compromise are safe harbor rules which allow sites with user-generated content to operate without being sued for copyright infringement perpetrated by the users, as long as they follow procedures to remove such content promptly. And end users typically aren't sued because that's bad publicity.
What that means for your "blog/website that i host myself?": as long as it never gets very popular (which is the most likely outcome), it will probably remain unnoticed anyway. If it starts earning real money, you'll get legal problems sooner or later that will shut you down unless it got so big so quickly that the copyright holders figure that they can have you make money for them. And if it involves user-generated content, satisfying the requirements to be considered a safe harbor is probably not done easily and should be vetted by a specialist lawyer.