No. Absolutely no modding or hacking is necessary to run Blu-Play games. Your console was designed for this!
(There is an advantage in owning a jailbroken PS3 though, because it lets you run Blu-Play games from harddisk, which means you don't need to burn a disc. But that is not related specifically to Blu-Play).
In short: All platforms that feature a Blu-ray player. See Platforms for a detailed overview.
You download the ISO, burn it to a BD-R or BD-RE and pop it in the discdrive.
If your PlayStation is rooted, you can also simply copy the ISO to the harddisk and mount it with webMAN or multiMAN from the BDISO folder.
Lots of options on the Xbox One: You download the ISO, burn it to any optical disc that'll fit. Can be CD-R, DVD-R / DVD+R or BD-R / BD-RE. Then pop it into the discdrive of the console.
BD-9 was sadly removed from the BD-ROM specs in 2011, so only a few older players actually support those variants. The Xbox One will play blu-ray content on any optical disc though, but that's not specific to BD-5 / BD-9.
Also consider: A blu-ray burner doesn't cost that much, and there's virtually no price difference between DVD's and BD-R's anymore.