Instagram has today released Instagram 4.1 for iOS and Android with new features, most notably the ability to import video from your library something that I myself have wanted for a long time, and something that Vine lacks. It makes no difference were you captured the video now, and once you select the clip you can trim it down to the exact part you want to feature in your Instagram video. You also have the ability to choose how you square-crop the clip. Instagram 4.1 also adds automatic straightening for iOS. Instagram says they have developed a "brand new technology" that straights photos. When shooting inside Instagram, you can tap the new Straighten button and it will correct it to be level. The straightening tool also includes a slider so you can rotate and adjust for straightening imported photos.
For Android users running Ice Cream Sandwich the ability to record videos is now possible.