Thought I'd get the ball rolling on the applications that I use the most on the Mac (excluding the obvious Apple ones such as Mail, Safari, iChat, iCal and the iLife Suite).
Camino as an additional web browser to Safari (for those websites that don't work correctly with Safari) - Camino seems to work faster than Firefox
Growl for notifications
Skitch for screenshots (not really necessary for newbies but a nice fun utility and could be useful on forums to show where they are having problems). Hope this comes out of invite-only soon.
Perian, Flip4Mac and VLC for video codecs and playing files that standard QuickTime Player refuses to play
iWork as a replacement for basic Microsoft Office functions
1Password (although Keychain Access can do most of the fundamental functions)
Adium as instant messenger (because it covers MSN, which lots of people are on in the UK at least)
Skype
Carbon Copy Cloner to make backups that allow you to get up and running much quicker than Time Machine if your systems goes belly-up (Time Machine has the advantage of incremental backups though so use that too)
Unison for usenet newsgroups and downloading (you'll need access to a usenet server too - that topic is for other threads)
MacPAR deLuXe for bringing the downloads from usenet all together
Vienna / NetNewsWire news reader (although people may be happy with the inbuilt Mail or Safari ones)
iStat Menus or
Menu Meters for seeing what's going on with your Mac (e.g. CPU usage, hard drive usage)
AppFresh to keep your apps up-to-date
iBank for personal finances (but there are quite a few alternatives - unfortunately, none as good as Microsoft Money for Windows)
MacTheRipper, Handbrake and/or
iSquint (plus
VisualHub if willing to pay for the excellent app) - for ripping DVDs and/or transcoding video content
AppTrap (free app deletion utility) or
App Zapper
Transmit for FTP
LaunchBar for fast app launching plus much more!
LogMeIn (for secure remote control of another machine when iChat or Back To My Mac are not a viable option)
Transmission for BitTorrent
TVShows for automatically getting latest BitTorrents of your favorite TV shows
FileChute for sharing large files with others
Audio Hijack Pro and
iShowU for recording sound and vision from the Mac
RapidoSerial for storing your applications' serial numbers and other details
Senuti for getting iTunes music off an iPod
TextWrangler as my text editor
The Unarchiver for extraction of RAR and other file extensions
MainMenu for troubleshooting the Mac
Of course, with the wonderful Mac platform, there are many alternatives to all the above...