Here are three of the major ones:
Inflation risk. Most bonds' payments are fixed. But prices of the things you need to buy keep on going up. The longer a bond's term, the greater the chance that the payout won't keep pace with inflation.
Credit risk. This is the risk that your bond issuer will be unable to make its payments on time or at all. U.S. Treasury bonds are considered to have virtually no credit risk, while high-yield, or "junk," bonds - issued by companies with weak finances - have high credit risk.
Interest rate risk. Though a bond's life span and interest payments are fixed - thus the term "fixed-income" investment - its overall return can vary based on changes in the economy and the markets. Bonds are traded just like stocks, so changes in the economy and the markets can cause bond prices to rise or fall. Bond prices move in the opposite direction of interest rates - that is, when rates rise, bond prices fall. The longer the term of the bond, the greater the price fluctuation that results from any change in interest rates. (Note that price fluctuations matter only if you intend to sell a bond before maturity, or if you invest in a bond fund whose manager trades regularly.)