As we move toward a future where fingerprints might possibly replace passwords, I see one issue. While passwords can be stolen, they can be changed by the owner after being notified of the security breach. However, fingerprints can be stolen, but they can't be changed. In this future, what happens if someone's biometric data is stolen? You can't very easily change your fingerprints.
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The answer depends a lot on your use case. Are you using a biometric to authenticate yourself to a remote HTTP server? Then if someone steals a binary representation of your biometric, they will be able to log in as you. This is why we like moving to 2-factor authentication instead of a single factor.
An example would be something you are (your fingerprint, or a digital representation of it) and something you know (your password).
If you are doing local authentication, the story is a little different. Attacker's options are: cut-off your finger and take it with them (see Minority Report where he used eyes instead of fingers), get a scan of your finger and try to replicate it on something the scanner will be able to read, or connect something between the reader and the computer doing the processing.
Even for local authentication, 2-factor authentication is often used. Your fingerprint scan might pull up a picture of you on the security guard's computer. Or a fingerprint and a PIN.