It is a great idea to get Renter's Insurance. Usually it doesn't cost much and it can save a lot of heart-ache if something awful happens.
And many leases require Rent's Insurance to protect both the Tenant and the Property. Ours do.
At something like $100-150 per year, it’s not
very expensive. We suggest you go to Clark Howard’s tips for help finding a good
coverage. Here is other info for renter’s insurance:
http://hotpads.com/pages/insurancecenter/rentershome.htm
And be sure to have your Landlord named as an "additional insured." It costs nothing extra, and will fulfill the terms of your lease.