The big advantage to making a living trust is that property left through the trust doesn't have to go through probate court. In a nutshell, probate is the court-supervised process of paying your debts and distributing your property to the people who inherit it.
The average probate drags on for months before the inheritors get anything. And by that time, there's less for them to get: In many cases, about 5% of the property has been eaten up by lawyer and court fees. To learn more about how you can avoid probate, see Nolo's 8 Ways to Avoid Probate.
Still, not everyone has to worry about probate, and some people don't need a living trust at all. To find out whether a living trust is right for you, see Nolo's article Why You May Not Need a Living Trust.