I wouldn't be harassing my European brethren in #Amiga.org chat right now if it weren't for Java.
I wouldn't be able to waste countless hours being entertained at
www.homestarrunner.com if it weren't for Java and Flash.
Flash, Shockwave, Java... critical pieces of the Internet experience. If you don't have it, stick to BBS's IMHO.
Another thing would be a simple, easy to use Windows file and print services client. (Mac even comes close to this now, there's no sense in avoiding it since most homes/businesses have it.
RE: Office Applications? I'm not sure. I use Word, Excel and Outlook at work constantly. They have their problems, but I'm in and out of them so much that they've become quite comfortable, and they're again the standard. I ordered Amiga Writer 2 recently and I hope to be able to make use of it at home, but we'll see.
Basically a decent current OS needs to be able to interface with my TV, DVR, Palm, Phone, Cameras etc with the same or greater ease as a PC.
Bluetooth, Firewire, USB2, Wireless Networking, Wired Networking, fully (And I mean FULLY) Multimedia capable.
And all "plug and play".
Oh, and it needs to be able to run World of Warcraft

If I could do this I wouldn't even own a PC at home.