The only types of bonds that are insured by the government are U.S. savings bonds. Other bond types, such as corporate bonds, are backed by the issuing entity and have no guarantee of value from the government.
U.S. savings bonds are often considered the safest type of bonds because they carry with them the full faith and credit of the government. A government bond is basically a line of credit taken out by the government from the bond purchaser, establishing a fixed value and rate of interest over a multiyear period. The bond value is figured into the country's national debt, and thus carries specific plans and guidelines for reimbursement after the agreed time period. Countries such as the United States have firm financial footing, so there is an incredibly low risk of the government defaulting on the loan.
Corporate bonds are seen as some of the highest-risk bonds, yet the bonds also offer some of the highest rewards. These bonds function like stock in that the company has complete control over how many bonds are issued and in what amount. The risk with corporate bonds is that there is no guarantee of repayment if the company files for bankruptcy.