I think MorphOS has quite many good modern programs. Odyssey is a great browser, MorphOS version of mplayer is the best movie player of all platforms, ShowGirls is great image processor, Scribble is great programming editor, there couldn't be easier CD/DVD burning suite than Jalapeno, Flacapella is just fine flac/mp3/other formats ripper, RemoteShell does everything you need for SSH2 usage, VPDF is modern PDF viewer, Jukebox is great little music player, there's Blender for rendering and video editing, Scriba is promising new word processor which can save for example to PDF and ODT, and lots of more.
There isn't that much modern games, but certainly much more modern than Doom or classic Amiga ones. For example Virtual GP 2, Knights & Merchants, Robin Hood, Quakes up to III, Return to Castle Wolfenstein, Homeworld, Warzone 2100 etc... and lots of SDL ports of all kinds of games.
And then all the best of classic Amiga software works too, there's lots of still useful software available for all purposes.