At the moment any PSP with firmware less than version 4 can be downgraded, and therefore custom firmware installed. However I still don't think any PSP3000's can be hacked yet.

A good list of models that can be hacked is here.

However while custon firmware cannot be installed on a PSP3000 model I think it can be run using HEN (save game exploit).
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I assembled my old PSP again yesterday (for info, it was disassembled in January 2008 ), and also put one of the latest cfw's again, the 5.50 GEN-B, or what is it called. Now it fully works again, is golden yellow, and perhaps I won't buy another one. Wanted to buy a slim one perhaps for the girlfriend.
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