My succulent has been growing sideways for a while. Today the planter tipped over because of the unbalanced weight. I moved the plant to give sunlight exposure from different angles but that didn't really help.
What is causing this and is there anything I can do to help it?
This is fairly normal behavior for these plants. As they grow, the stems get longer, and since the leaves are full of water, the weight of the top of the plant pulls the stem over to one side. It's not really indicative of a problem, but it can be a little annoying.
You've got a couple of options as I see it:
You can get a heavy, possibly ceramic pot that won't be so easily tipped over, and either re-pot the plant into it, or place your existing pot inside of it. The plant will continue to grow as it has been though, and the dangly bit will become even danglier over time.
You have a new shoot growing at the base of the older stem. You can take advantage of this and propagate the plant to get a second (and a third, fourth, etc. if you want) plant out of the deal. You can cut the long stem off near the base of the plant, using a clean knife or shears, trim off some of the excess stem and set the pieces aside for a day or two to let the stem ends callus over a bit. Once they've callused, you can try rooting the trimmed stem cuttings, end rosette, and even any fallen leaves separately to see if they take. You place each cutting in its own small pot, or next to each other in a larger one, and wait to see if they root. Many of them will, and you can soon find yourself with a whole grove of plants.
The cause is usually not enough light, or the light is very directional (for example if the pot is near a window). The remedy is to turn the pot regularly (i.e. every day or two) to keep the plant growing straight. You can't "straighten out" a plant that has grown as twisted as your picture, though. Best to start again from cuttings, as in the other answer.
If you really want to "start from scratch" with this type of succulent, gently pull a few of the lower "leaves" from the stalk and put them somewhere clean, dry, and well-lit (but not scorched with strong direct sunlight). The don't need any compost, and in fact they are less likely to rot or get other diseases without any compost. There is enough water stored in the old "leaf" to start off the new plant. Pot them up when they look like the picture, which may take a week or two.
(Image source: http://gardeninggonewild.com/?p=24797)
