Here are some of my favorite apps:
mozilla (also avaliable for windows, btw)
http://www.mozilla.org
blender, a 3D rendering program, free but not open source
http://www.blender.nl
the gimp, a program with photoshop like capabilites, open source
http://www.gimp.org
nmap, a portmapper. don't know much about it but apparently its what everyone uses for that type of thing
http://www.insecure.org/nmap
wine, lets you run (some) windows apps
http://www.winehq.com
gkrellm, a nice little program that shows you system stats
http://gkrellm.net
xmms, a skinnable mp3 player
http://www.xmms.org
for email i use balsa
http://www.balsa.net
also if you are into gaming, check out some of the ports from windows games by loki games
http://www.lokigames.com
for office software, i don't use an integrated 'suite'
i use a word processor called abiword, which is open source, but has a word like interface and a spreadsheet called gnumeric. This is only because of space considerations on my computer (i don't have room for staroffice) but i have friends who use staroffice and love it. if you are more into kde, then they have a whole office suite called koffice also. lastly there is corel wordperfect for linux that is free for non-commercial use.
abiword:
http://www.abisource.org
gnumeric:
http://www.gnome.org/projects/gnumeric
staroffice: just go to sun.com and follow the links
koffice:
http://koffice.kde.org
wordperfect:
http://linux.corel.com/products/wp8/download.html
there are also several hotline clients for linux, the one I use is gtkhx
http://gtkhx.sourceforge.net
Probably some of these apps came with your distro, so you won't even need to download them hopefully.
and there is tons of other stuff. check out these sites for more:
cnet's linux section:
http://www.download.com/linux
tucows's:
http://www.tucows.com , click the linux link
freshmeat:
http://www.freshmeat.net
sourceforge (only open source):
http://www.sourceforge.net