If you mean redownloading stuff you have from one PS3 to the next, then it depends.
If you use the same account, everything transfers from what you have on your download list on the PSN.
However, you cannot do this beyond a certain number of devices. It used to be that users were allowed up to 5 systems to be activated for one PSN account. However, people exploited this ("game sharing") and it was patched to only 2 (the current system).
This means that if you try to redownload your PSN purchases on more than 2 devices that use the same PSN account (PS3, Vita, PSP, etc), it won't work.
Just be sure that you're not using your PSN account on multiple devices. If you are, you have to deactivate a system or two. That can be found here:
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EDIT: crap, I completely misread your post. Yes. All purchased items on one PSN account on one PS3 is shared among all other PSN accounts associated with that same system.