You cannot log in without the password if the owner of the account has opted to make it private, which is what most people do for privacy reasons when they're linking the pictures to sites where they don't want all of the content revealed.
I once made the mistake of forgetting to make an account private, and risked people seeing a majority of the content, some of which were photos from trips I had been on and friends I visited and such, which wasn't meant for public consumption. Fortunately, I noticed the error rather quickly and the pictures weren't compromising.
I'll take this time to remind everyone who uses photobucket and similar services, to make SURE you have the privacy and password settings on if you want the account to be secure. Otherwise, everyone who wants to see your pictures can simply load the page in their browser and access the gallery from there.
If you're using a service that doesn't have these security options, then don't use it, if what you're uploading is personal.