I used to use a 261MB Seagate HD... And that was with Win95 on top of it. Usually had about 20MB free.
I couldn't have anything installed... All I had was IE 5, Win95 and ICQ 99. Oh yeah, Outlook Express too. Had a tiny bit of room for web pages, but not much.
That was in the days of the P83. Now I'm using a 412.5MHz K6-2/350 w/96MB RAM and (best out of all of these things) a 20GB Quantum Fireball Plus LM. :Q The Quantum made the most massive difference, as a single upgrade.
Do we need these large hard drives? No. That answer is no, for everybody. Now, if you change the question, that's a different story.

If the question was "do we need these large hard drives to store our apps, games and MP3s?", the answer for most of us would most definitely be yes.
So far, with my 20GB hard drive, I've never been able to fill more than 11GB... But, I don't have all that much stuff to install. At the moment I have 1.38GB of MP3s, Windows 2000 Professional, Windows 98 and BeOS triple-booting, as well as Quake III Arena and Unreal Tournament, IE 5, Outlook Express 5, the usual. I have several different installations of ICQ (to keep 2K and 98 from messing each other up.. I have it all on the same partition, a real fatty FAT32)... ICQ98, ICQ99b, ICQ2000a, ICQ2000b...
Anyway, right now I have 11.6/19.1GB free ("20.5"GB hd.. ha). Not bad... Still got plenty of room, and my hd is several months old!
-RSI