I'm going to be a fuddy-duddy and say: most of these apps are
not essential for the Mac. Lots of them are nice, but you can skip them entirely when you're just getting started.
Here are the ones I consider absolute essentials for my daily work:
MegaZoomer - http://ianhenderson.org/megazoomer.html - lets you full-screen zoom any application. That mixed with TextEdit gives you the best word processor you'll ever need.
Quicksiler - linked all over - this will fill in every hole you have in your computer usage. I use it to fix a lot of shortcomings in iTunes, for instance, and while I don't use it as insanely as some people do, even light usage makes your life a lot easier. It's also a full-featured file browser, which is excellent.
Perian - http://perian.org/ - makes your life a lot easier when you're watching videos or listening to music, without forcing a reliance on the ugly VLC.
GlimmerBlocker - http://glimmerblocker.org/ - Unless you use Firefox, this adds every feature you'll need to every browser you've got. (Firefox is an awful browser that rebuilds a lot of Mac features from the ground up, and so it isn't affected by this.) It blocks ads (selectively, so you can allow the ads you don't mind), blocks entire sites, and adds retroactive functionality to sites. The big one for me is the Youtube downloader.
Growl - http://growl.info/ - This one's really easy to abuse, but if you set it to notify you of all the really important things - FTP file uploads and long processes and so on - then you get a very nice way of keeping yourself informed of all your computer's goings-on.
Those are the ones that I absolutely need for my Mac. Here are the ones that are obscure-ish and rarely recommended and yet are terrific:
Max - http://sbooth.org/Max/ - converts every format but wma, so your library stays neat and organized without any complaints about iTunes.
Freedom - http://macfreedom.com/ - disables the Internet, so you can't procrastinate at all.
FuzzyClock - http://www.objectpark.org/FuzzyClock.html - makes your clock much more humane.
Chax - http://ksuther.com/chax/ - Fixes a few things in iChat to make it an acceptable chat system (I really dislike Adium for a number of reasons).