Have you clicked on a page that says "You agree not to save anything from this website"? No? Read on.
The pictures are displayed by means of a JavaScript that then prevents you to save them. Those are really silly and annoying scripts aimed to discourage saving images from your web browser. You can, however, bypass them easily if you wish to and I will even tell you how:
Just view the source of the page and find the code displaying the image within the HTML. Then build the URL for the picture you want directly and VIOLA - you can save the image with no silly scripts to annoy you.
About the legal issues:
ANYTHING you see online is FREE TO SAVE AND DOWNLOAD unless you have agreed not to do it. Noone can jump out of nowhere and tell you "this is illegal to save" as they have made it publically available to you, and everyone else on the Internet. In fact, YOUR web browser will save every image and every webpage you browse to regardless whether you wish to save something from there or not. It is called caching and serves to not only to speed your access up, but also to prevent the server from being overwhelmed from serving repeated requests from clients. It's a mutual benefit.
In some cases it goes further than this: unless websites instruct otherwise, Internet Service Providers will sometimes cache content clients often browse to so that they can provide you with faster online experience as well as to cut down on external traffic. This is also perfectly legal as all they do is cache something that is already made publically available.
THIS IS WHAT IS ILLEGAL:
It is illegal to take ANYTHING you haven't created yourself and do anything with it without the copyright holder's permission.
This means you cannot upload your saved images to other websites, you cannot present them as your own, you cannot derive something of your own from them and claim it as yours, you cannot charge people to see them, and a lot of other stuff. This is common sense.
In some instances, however, copyright holders will say that they grant you privileges under some licence, for example GNU or Creative Commons. This means that in some cases they might allow you to post their image as long as you do something for them, like link back to them, acknowledge their copyright etc. This is between you and them.
In short: read the licence.