I use Slackware for:

web server
mail server
DNS
ftp server
browsing
developing web sites and applications
amusement

I am a linux newbie. Slack is my first.

I use/want to use Slackware for:
Learning about Linux
Media server
Uni work (I do programming in Java, LISP soon to move on to C etc)
As a DVD player (via my TV out - if I can get these Nvidia drivers installed)

I use slackware on Desktop, Laptop and Server.

On desktop, I use slackware for:
Browsing
Word processing/spreadsheets
DV Capture and video editing
Music Management/Playing
IM/Email
Torrents
Little bit of programming (I should say scripting)
Leaning about databases (postgresql and mysql)
and just about anything I can think of.

On laptop (which belongs to my wife):
I've managed to squeeze Slackware on that in the hope that she might start using it.
Mainly used for browsing/IM.

On Server:
It's Apache, MySQL, gallery2 and wordpress for my personal site on headless dell box. The box used to be my desktop before I made it a server and built a new desktop.

Tux,

I use it to replace Windows boxes at work.

irc - irssi
music - cplay
web - ff
torrent - rtorrent
mail - pine
1337 haxoring - vim

Just everyday work...