Disclosure: I work for AgileBits, the makers of 1Password.
The safety of your 1Password data on Dropbox depends on the quality of your 1Password Master Password.
The long answer is just an explanation of the short answer and a couple of other things.
We designed 1Password under the assumption that some people would have their encrypted 1Password data stolen. Whether it is stolen from their own computers (someone walks off with a laptop) or from something like Dropbox doesn't really matter. It is possible for the data to be stolen, and this is why it is encrypted with keys that are encrypted with keys that are derived from your Master Password.
Now we make heavy use of PBKDF2 to slow down automated Master Password guessing in the event that the 1Password data is captured, but PBKDF2 and the like only present a speed bump to the attacker; it does not provide a solid barrier. So it is important you pick a good Master Password.
More than five years ago, we offered some advice on picking a good Master Password in Toward Better Master Passwords. This advice was picked up by XKCD and made famous, but it satisfies what I call the Kantian Principle of password creation advice: Password creation advice should remain good advice even if everyone follows it.
Do not reuse your Master Password. In the three known (to us) cases in which someone's 1Password data was compromised, the user used the same password that they used elsewhere for both Dropbox and for their 1Password Master Password. Don't be like them.
At the risk of descending into a sales pitch, I should point out that with a 1Password account, you no longer need to manage your synching through something like Dropbox. We have even designed this with Two-Secret Key Derivation (2SKD) so that even if your data is captured from our servers, an attacker would not be able to launch a password guessing attempt against that captured data. Please see our white paper (PDF) for details of how that is managed.
But as the question was specifically about 1Password data on Dropbox, let me return to that ...
OPVault v Agile Keychain
Depending on when you started using 1Password and on which platform, you may be using the Agile Keychain format on Dropbox. The Agile Keychain Format was designed nearly a decade ago and has some shortcoming for a today's world. It exposes much more "meta data" than is appropriate and it does not include any tamper detection.
So the one thing I would recommend to those synching 1Password data with something like Dropbox is that they switch their sync format to the OPVault format. OPVault encrypts far more meta data, and uses authenticated encryption to defend against a wide class of attacks that involve tampering with the data.
But with either data format, the safety of your 1Password data depends on the quality of your 1Password Master Password. Make it unique, strong, and memorable. And you may wish to write it down and keep that in a safe place because there is absolutely nothing we can do if you forget your Master Password.
With a 1Password Account, a good Master Password is still needed to protect you if data is stolen from your local machine, but 2SKD does protect you if data is stolen from us.