Where to start...I guess I can just make a list of awesome apps that are, well, awesome. I will only list apps that you might not know, browsers, social apps, and the such will not be listed as you probably already know they exist(ie. FireFox, Twitter, Filezilla, etc.)
Keka(good file archiver)
MAMP Pro - Mac, Apache, MySQL, PHP. Great for a development installation of xF among other things.
MarsEdit - In case you plan on running any blogs, great interface.
Mactracker - Just a good tool if you are interested in the history of Apple.
BetterTouchTool - Allows you to specify more touch gestures.
mSecure - Wonderful password-keeping tool.
Notational Velocity - Works wonders for taking notes and can be integrated with SimpleNote so that your notes will sync to the SimpleNote website and can therefore be accessed cross-platform.
VirtualBox - Works just as well as VMWare Fusion IMO and it is free.
ScreenFlow - If you plan on making tutorials or demonstrations then this is your friend!
Dash - $20 for the full version(had to say this because it is a sneaky app that disguises itself as free) but it is great to have all your programming language's docs in it as well as snippets.
Coda 2 - Useful for coding but I mostly use it for the reference books it has because I already have DreamWeaver.
Growl - You can use this as a temporary replacement to Mountain Lion's notification system.
HandBrake - If you have any .avi's or any other incompatible video format for Mac then you might want to use this to change them to something that is compatible, eg. .mp4.
Friendz - If you're an Xbox junky like I used to be or you just want to be able to keep in contact with friends then this is the app to use, works with Growl

.
Adium - Someone mentioned this before, great messaging app.
Remote Mouse - Turn your phone into a mouse for your Mac.
Pulp - Great way to organize your news feed(s).
iWork - I personally favor iWork over Microsoft Office but to each his/her own.
That about sums it up, good luck with your Mac!