I have the same issue with some of my Aloe Vera plants, although most Aloe plants really don't have a very extensive root system at all. I've found the easiest way to keep both me and the plant happy is to set the root far enough down into the soil so that the very bottom leaves of the plant are actually resting on the soil. Angle it, if needed, so that the plant itself is straight upright. You can always add support for the plant by placing small tree branches or a miniature trellis on the side that it wants to fall toward, to help it stand up straight.
Be sure to plant your Aloe Vera in proper soil -- see this article for additional information: