(NOTE: Looking for info about Aloe Vera pups/ shoots? See here)
Unfortunately, the only houseplant I have right now if aloe vera, or at least some type of aloe.
These are really easy to propagate, meaning start growing. (Usually plants propagate by seeds or cuttings.) Aloe vera sends out little parts of itself that come from the base called "pups", sort of like if a tree sent out a branch from its base. They do this a lot, too, especially when they are old. Rip off the "branch" of aloe vera and stick it in a pot...and whella, it'll grow. Seriously. Just rip it off- but again, think of the tree. If I were to remove a branch from a tree, I wouldn't go cutting down the trunk- try looking at the pictures, that should help.
Try to get a nice green pup, about 3-4 inches long. See if your neighbor has one. If you can't convince them to give you a pup, tell them it's actually healthier for the plant if you remove the pups (less competition for resources).
The tricky part is when you stick it in the ground the plant will start turning a dull purple-brown color...during this stage it doesn't grow. It's trying to get roots and stuff again, so just give it some time. Could take a couple months, actually. But when they start turning green again you know you've gotten past the hard part.
They're supposed to be good medicinally...rip off a leaf and break it open so you get the juice and you can rub it on your sunburn or whatever burn you have. But I haven't been burned so I don't know about that. And it's also supposed to be good for your body if you eat it- but I think it tastes bad. It also moisturizes your skin; they sell aloe vera facial masks.
Don't water them too much, though. They're succulents, same as cacti. Note: If they turn purple-ish, and there are brown shriveled tips or brown shriveled leaves that are dying at the bottom, you haven't watered it enough. Again, don't super water them- it will take a little (actually a lot) of time (roughly a month or two) for it to look nice and green again.
Let me see if I can get a picture of mine up.
NOTE: Clicking on the pictures gives the full screen view.
EDIT 4/28/09: More pictures.
Aloe with 2 pups- can you see one near the front, and one on the let just barely peeing out? When they get about 3-4 inches tall, I can pull them out and plant them. All I have to do is yank them from the base.
Aloe that's purple- I thought I had too many so I pulled this one out of the soil (you can sorta see how the roots aren't rooted).
Aloe with pups (2) on the left...they're almost ready to be pulled off. Again, just yank from the base. You could use scissors, if you want.