Grids is a very effective Instagram client for desktop computers. While it doesn't let you post pictures from your computer, it does let you view posts from the people you follow, see new post notifications, and 'like' or comment on any photo in your stream.
The Grids interface is well-designed, displaying all the posts from the people you follow on a simple grid, though there are more display modes available with the paid Pro version. Just click on any picture or video to take a closer look. From there, you can 'like' it, leave a comment, or view the profiles of commenters on the same picture or video. The customization options let you adjust the display size of the images, choose whether you want the videos to play automatically, and even change the background color of the program if the default black isn't your style. You can also turn on notifications within the program with just one click.
Grids is a highly recommended Instagram client. Though its free version doesn't include every possible feature, it does have all of the most important ones. You can't search for hashtags, for example, but you can view and comment on everything your friends post and manage your own account.