First, I am not a lawyer and I don't play one on TV. This is not legal advice, this is my opinion.
If I leave my bicycle in my front yard, and you walk by, can you take it? Not legally. It's my property, even if I didn't lock it up. If it's in the trash can, can you take it then? Sure, I've abandoned it. What if someone else takes my bike from the front yard and puts it in the trash and THEN you come by, see it in the trash, and take it? Technically, it's still illegal; I did not abandon it, even if you do not know that.
Well, let me put it this way. I am a photographer. I post many of my photographs on Flickr, with a 'Creative Commons' copyright (mine is listed as 'Attribution-NonCommercial-NoDerivs'). That means I am giving everyone the right to use my photographs for 'non-commercial' use, if they give me attribution and do not make other images using my images as a starting point. That means you could put one of my photos in your blog, for example, as long as you say you got it from me (attribution) and you don't make money on it (you do not sell my image) and you don't alter my image.
Since it's my image, I have the right to put whatever conditions I want to on the use of it. I could, if I wanted to, make it a standard copyright, no use at all. That means no, you can't use it, not even for personal use, without my permission. It doesn't matter where you found it.
There have been a couple of misleading statements in this thread about copyright. First of all, in the USA, a work is copyrighted automatically. When I take a photograph, it is copyrighted by me, and I don't have to do anything. It belongs to me, it's my property. And I can enforce my copyright in court; I do not have to file a copyright registration with the government in order to do so.
However, copyright law in the USA says that if I want to sue for punitive damages and not just actual damages, then I have to have registered my copyright prior to the infringement. It's easy to do and doesn't cost much, but most copyright lawyers won't take a copyright case unless the copyright is registered. If you don't register, you still have the copyright, that's automatic. I've had a few arguments with people who think if you don't register your copyright, anyone can use it. They are wrong.
And I can prove they are wrong, and I can prove how well I can defend my copyright. Every couple of weeks, I scan Google using a special tool that finds people using my photographs from Flickr. If it is a commercial site, I send what is called a DMCA Takedown Notice to the service provider of that website. You know what happens next? The website goes DOWN. The owner of the website it informed of the claimed infringement and is told what they have to do to get their website back (remove the image or pay me for the use of my photo on my terms). If they remove the image or write me a check, then I give the ISP permission to bring the website back up. I don't have to go to court, I don't have to sue, I don't have to file a police report. Use my photographs commercially without my permission, and I'll shut your website down (assuming it is in the USA).
So when it comes to what you find on the internet, I don't think you can automatically assume that whatever you download is yours legally. I can think of many cases where that is not the case. Sometimes it depends on how you use it, but sometimes it is just not allowed, period. It all depends.
If in doubt, consult an attorney. No one here, to the best of my knowledge, and including myself, is qualified to dispense legal advice.