There's a great media system for the Xbox, but other than that I can't think of a single other even modestly popular application to come out of console hacking.
That depends, do you consider emulators an application? My Wii is homebrewed and I have to say it's MUCH more fun playing retro games on my Wii than on my PC. And XBMC is not the only great program of this sort. I use WiiMC all the time. There's also some cool MOD players, Shoutcast players, etc.
I'd like to put this thought out there: the whole idea of running a desktop OS on a game console has very little traction and even less ROI.
I'd agree that desktop OS's are not well suited to consoles. Consoles are entertainment systems so they're well suited to entertainment apps. However, having said that, I would not be at all opposed to having AROS on a PS3 so that I could run AMC. I'd probably also use OWB on AROS as well (yes, the PS3 browser really is worse than Amiga web browsers). I doubt I'd ever want to do wordprocessing or spreadsheets on the PS3 but, theoretically, the AROS user interface could be modified to work well with a PS3 controller on a HDTV.
It would actually be very nice to boot a PS3 into AROS with a simplied interface that displayed the weather, showed RSS and twitter feeds, showed when I had new email, etc. And where I could easily stream music/video, play slideshows, run emulators to play retro games, and do some basic webbrowsing, and perhaps play some AROS games. Why does AROS need to remain a "destop" OS? In fact, maybe a unified goal of trying to design the best "console" OS could help encourage more development in AROS.