Besides being able to embed Instagram photos on your WordPress.com site, I just realized that perhaps you don’t know that since Instagram now lets you log in on its website to view your friends’ stream and your profile, you can also create a badge to put on your WordPress.com website.
After you log in to the Instagram website, click on your username in the upper right corner and then “Badges” from the drop down menu there. Select your badge and copy only the last part of the code.
<a href="http://instagram.com/yourusername?ref=badge"><img alt="Instagram" src="//badges.instagram.com/static/images/ig-badge-view-24.png" /></a>
Paste that into a text widget and save. (Your code will look a bit different depending on what icon you choose.)
Alternately, you can save the badge you wish to use, upload it to your Media Library and then use it in an Image Widget, linking it to your Instagram user profile.
Also, there is a discussion in the forums about using the flickr widget for instagram images, but be warned it does not always work as expected.