Symmetric encryption is problematic. It's well and good to say, "Just use Waq3$f^t>p~6pWr as your password, and you're fine!" but you're leaving a huge door open to social engineering and user carelessness.
So I would say, hypothetically, assuming a first class password, you're okay using symmetric key encrypted zip programs that offer proven encryption algorithms, but in the real world the dependence on password strength is a huge weakness.
@Akira: I didn't say it was bad, I said it was problematic and it is. With public key (asymmetric) encryption, you have a constant level of security. If you have a 1024 bit key, your data is 1024 bit encrypted.
With symmetric key encryption you can have godlike security (1024 character password) or worthless security (1 character password), and you have no control over which you're going to end up with.
(Note: I didn't bother to talk about compromised keys because that effects both methods equally)
@Nifle: Agreed. Key exchange is the problem with public key crypto, but it's a much more reliable method. I tend to recommend against symmetric key encryption because it makes people think they're safe, when they may not be.
@Akira: Not sure what you're talking about, frankly. Just because private keys are often secured with a passphrase as an additional safeguard doesn't mean that symmetric/asymmetric encryption is "using symmetric keys for the real encryption." Asymmetric encryption uses two different keys: one for encryption, one for decryption. And calling higher bit encryption snake-oil is disingenuous at best: if that were the case then aes128 would be the same as aes256.
And comparing a one-time pad to any kind of machine crypto displays the worst sort of ignorance. They're secure because they're pure random noise of the kind that computers, by their very nature, are unable to produce. You're saying that, because one kind of symmetric key encryption is secure, then all kinds of symmetric key encryption are secure, which is an utter fallacy. And worse, you're holding the otp up against asymmetric encryption when they have the EXACT same key exchange problem!