Instagram has introduced web embedding letting you share your Instagram photos and videos across the web, the way you would a YouTube video.
Here is more from the Instagram blog:
Now, when you visit an Instagram photo or video page on your desktop web browser, you’ll see a new share button on the right side of your photo (just under the comments button). Click the button to see the embed code. Copy the block of text it gives you and paste it into your blog, website or article. When you hit publish, the photo or video will appear.
The feature is only available for photos and images that are available to the public. If you have your account set to private, this feature is turned off.