You can create your own virtual Lego character at the official Lego Movie website. If you want a tangible character to play with, then check out Mini Figs, a company that will create and ship you a Lego character who looks just like you or a loved one.
Virtual Lego characters can be made on the Lego Movie website by customizing the various parts of a Lego person. You choose its features such as head shape, eyes, eyebrows, hair, clothing and more. You can even set the "scene" your character will be placed on, as well as the character's name. You can send the newly created Lego person to a friend, download it as wallpaper and play the various web-based games available on the Lego Movie website.
Mini Figs is a U.K.-based company that allows you to customize a Lego character, although it is not affiliated with Lego. It offers hundreds of combinations so you can create a character who looks just like you, or create one as a gift. Like the virtual versions, you choose the different components and accessories to make the figure unique. You can even add a name or message to the back of your Lego person. Because each character is custom-made, shipping can take several weeks.