I'm no iPhone expert, but I've taught computer security at a grad level before.
As far as I can tell, jailbreaking can make your phone more vulnerable to attack.
The ssh attack that's been going around recently, it's a really simple attack - it just assumes that the owner never changed their default root password. That's really just stupidity on the part of the owner.
*However*, in the future, someone could find a vulnerability in the SSH server on the iPhone, and exploit that to do something nasty with your data. (Probably not likely though.) This is not to say that the iPhone is secure if you don't jailbreak it. I'm sure there are services in the iPhone with uncovered vulnerabilities too. (Didn't they discover some SMS vulnerability or something a while back?)
On the iPhone, the general security model seems to be what they call a "chroot jail" (from where the term "jailbreaking" comes from). Normal apps on the iPhone are installed in a way that lets them only see a tiny part of the filesystem on the iPhone. So it won't let you look at any other application's data. Jailbreaking is all about getting away from this limitation.
So, yes, it is entirely possible if you install a nasty app through cydia, it will go ahead and do something mean, like going through your 1password information.
Of course, there's plenty of intrusive stuff apps can do too, and be approved by the Apple store. Like, harvesting information from all the contacts on your phone, for instance.
But going through a jailbroken phone is not your only means of attack. It might even be easier to just attack your computer directly. If you could be convinced to run an executable file (like, say, blackra1n) the author of the executable file could just take control of your computer. If they were after your 1password information, I bet there might be a way of digging it out of iTunes backup. Or maybe just install a keylogger on your computer to grab all your passwords.
I'm sure that's not the answer you want