There's an endless list that you'll get from different people, but here are a few old standbys:
Adium - Chat client that handles almost any account you can think of.
Quicksilver/Google QuickSearchBox/Alfred - Application launchers with a wide variety of different features. Pick your favorite (or use all three like I do).
AppCleaner - Remove applications and deletes .plist files and anything else associated with the app.
Audacity - Free audio editor.
Blender - 3D modeling software.
Bodega - An app store for your Mac, reccomends applications in many different categories.
Bowtie - iTunes controller/HUD with HTML/CSS customizable skins.
Candybar - Allows you to change system icons, docks, etc. (Not free, but comes with a long enough demo period).
Cinch/SizeUp - Simulates the "snap" feature on Windows, allows you to resize windows to half screen/quarter screen.
Colloquy - IRC client.
Cyberduck - FTP manager.
Dockless - Removes Dock icon from applications.
Firefox - Duh.
GIMP - Free image editor (requires X11 and isn't all that user-friendly).
GrandPerspective - Allows you to view all files on your hard drive graphically.
Growl/GrowlTunes - Shows device/internet connections, application events, and loads more.
HandBrake - DVD ripper.
HimmelBar - Launch applications from the menu bar.
Hulu Desktop - Front Row-esque Hulu player.
OnyX - Cleans up system files, .plist files, etc.
OpenOffice - Microsoft Office clone from Sun Microsystems.
PandoraMan - Desktop Pandora client.
pomodoro 2 - Great timer if you're a fan of the Pomodoro method.
Skitch - Image uploader with handy editing capabilities.
Spirited Away - Hides applications after a set period of time.
SuperDuper! - Disk copier (great backup utility).
TextWrangler - Good text editor for code and HTML.
Think - Creates a backdrop with a single application shown (for focusing purposes).
Transmission - Torrent client.
twhirl - Adobe Air Twitter app.
UnRarX - .rar unpacker.
uTorrent - Another popular torrent app (supposedly the fastest).
VirtualBox - Virtual machine creator.
VLC - Plays almost all media files.
Sorry about the long list, but that's my freeware list and I can attest that they are all great applications.
About the account question, you shouldn't need to worry about working on an Administrator account. If the computer needs to do anything that requires clearance, it prompts for Admin credentials, no matter where you are. You can set up the account if you feel like it, but I wouldn't bother. I work in an admin account by default, and I've had no problems with it.
