How are those photos that you can see the extremity of the lens taken?

There are a lot of photos where you can see the photo and that circle of the extremity of the lens. I know it's something called fisheye, but there are some photos where you don't see it. I'm thinking about buying a Nikon D3100 and it has the fisheye mode but in some photos it's just a photo more rounded. I just searched for a fisheye lens and the result was the same.

Here's some photos of what I'm talking about (the rounded photos):



http://upload.wikimedia.org/wikipedia/commons/e/e0/Alpine_A110_fisheye.JPG

And what I'm looking for (the extremity of the lens):



http://ccaafloripa.com.br/novoblog/wp-content/uploads/2012/06/fs-lomo-fisheye8.jpg



http://shop.theclickshop.net/wp-content/uploads/2012/06/lomo_fisheye_lensflare_market.jpg
Added (1). If you can't open the links just copy them and paste on the url bar xD

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