Do you mean which models are capable of reasonably playing 1080p content, or which ones have video cards capable of outputting 1080p to a monitor?
All modern Macs with DVI output can output 1080p.
Any dual G5 or dual-core Intel Mac (sorry Core Solo mini owners,) can play back 1080p flawlessly. A Power Mac G4 upgraded to dual-processor 1.8 GHz or greater SHOULD be able to do it, but since that was never an official option, Apple doesn't say so. (And I've never seen any tests of it.)
P.S. I've tested my MacBook Pro (see sig) with one core disabled, and it did drop frames on the biggest 1080 QuickTime trailers.