Download This! Free Essentials for Macs.

NOTE:
All of the following are free

1. VLC(VIDEO PLAYBACK): It plays every video file known to mankind, so when Quicktime fails you, which it will, never fear: it will play in trusty ol VLC.
   
2. Firefox/Camino/Opera(BROWSERS): these are all great browsers for different reasons. In short, Camino is super lightweight/fast and Opera is super customizeable as is Firefox with its many extensions. Try em all and see what works best for you(including Safari). Firefox is the best bet IMO, but Safari is also great for most users.
   
3. Flip4Mac(WMV PLUGIN): a plugin which allows those annoying windows media files to be played on your Mac. Trust me, you'll need it, some companies believe think everyone is running IE7 and they're 70% right.
   
4. Menu Meters(MAC SPEEDOMETER): curious how those dual core processors are performing? Or perhaps you are curious to see if that 512MB of RAM is sufficient? Menu Meters gives a nice view of how your system is performing. I recommend expressing the processor as a percentage and your dual core chip as 2 separate indicators(right now they're both at 4%).
   
5. Monolingual(REDUCE CLUTTER): your mac comes with hundreds of megabytes and even gigabytes of language support you don't need; Monolingual removes these files. I saved 2.5 GB on my system! Just be careful and read the faq before running.
   
6. Onyx(SPEED UTILITY): Kind of like Disk Defrag and Scandisk for PCs, a nice app that cleans all the files that accumulate as well as repairing permissions an much much more. I consider this no brainer; run it at least once every few months and you'll likely notice your mac runs a little snappier. Also, if you have a noticeable slowdown, 9 out of 10 times you just need to run some maintenance scripts and Onyx make that task a lot easier than typing commands in the Terminal.
   
7. Limewire(FILESHARING): With a good internet connection, you'll be downloading music faster than you can say Ted Nugent. No ads, spyware, popups and good integrity...just make sure the file your downloading 'makes sense': That 642 kb bile is NOT the latest episode of LOST. This is the easiest way to get movies and music but not necessarily the best(see below).
   
8. Transmission(BITTORENT FILESHARING): If you need to download full albums, seasons of tv shows, or feature movies...this is the best way to do it. The only problem is it may require some tweaking to get it to work at a good speed. This app is lightweight, simple and effective.
   
9. Mac the Ripper(DVD RIPPER): If you wanna make backups of you DVDs or rip them to your hard drive using the original DVD file structure, just download this bad boy and it removes the encryption in one easy step. On average it takes about a half hour to rip a feature length DVD.
   
10. Audacity(AUDIO TOOL): I use this program to crop songs for music videos or make
    ringtones on my phone but there are more features and its simpler than Garage Band.
11. Handbrake(CONVERT DVDs TO ANY FORMAT): Easily converts DVDs into your format of choice. Includes a lot of encoding options such as video codec, framerate, bitrate, audio settings etc.
    
12. Super Duper(BACKUP UTIL): Nice app that will make a perfect copy of your current system. Backup, what's that, you say? Required. I don't care if you have a Mac, your hard drive WILL FAIL you someday(my friend's did 6 month after I got her a backup drive). If you don't have a lot of files, at least put those important documents on a CD/DVD/USB drive at a minimum.

Hope this helps!

BTW
Version Tracker, Softpedia, are all good sources for apps; check em out.