Back in the summer of 2002 I bought an aloe vera at a market. I left it in the boot of someone's car and nearly killed it but it survived. I nearly killed it during another summer and revived it again and the poor thing has been harassed to within an inch of its life by snails many times. But still my aloe vera continued to grow and thrive and after about 3 years of ignoring it I decided to repot it and propagate it (a plant as strong as this needs to be propagated). I took about 20 babies off the mother plant. The large, brown one, falling over to the left was being thrown out by someone at work because they didn't like it's organic shape, so of course I rescued it.
How to propagate aloe vera:
Carefully take your aloe vera out of the pot/ground and gently shake the soil off. From the main stem of the mother plant, you will notice many smaller offshoots coming off the bottom of the stem. Simply separate these offshoot from the mother plant, taking as much of the white root with it as possible. Place the offshoot in a pot of soil/sand or cactus mix and water well (adding the sand assists drainage so they don't get root rot). Warm weather and water will definitely help your aloe vera take off.
This photo is a few weeks after they were repotted, and you can see the leaves are fairly brown (there's a happy looking sage on the right though!). I've found this is common after propagation but with regular watering it clears up within a month. We've just had some more rain and they're now looking very green again.