You lock the doors to your apartment, so why wouldn't you lock your voicemail? You're just as liable to be a victim of theft from a fraudster getting into your voicemail inbox. And if you think password-locking your phone protects you, think again.
If you're calling your voice inbox from a different number, like maybe at work, you enter a (frequently 4-digit) passcode to get access to your messages. But if you call from your own phone and you're not prompted for a code, you're vulnerable to being the victim of caller ID spoofing.
Using a service like SpoofCard, you can easily change your outgoing caller ID information. It's endlessly useful for pranking your mom into thinking the police are calling, but also can be used by thieves and other shady strangers to get access to your phone's voicemail.
AT&T, Sprint and T-Mobile don't require cellphone customers to use a password on their voice mail boxes (Verizon does), but that doesn't mean you shouldn't. If an unsavory individual got access to your voicemail, they'd learn bits of personal information about you. Probably not enough to take your identity down alone, but it's certainly plenty to cause some damage. Your messages can reveal what bank you use, where your home mortgage is loaned and what your birthday is.
Since it's so easy to do, just take a second to set a password lock on access to your voicemail messages. And please, whatever you do, don't go with "1234" or any of these Most Common iPhone Passcodes.