When I bought my first Mac I'd been using a Windows laptop for a long time to do web and graphic design and writing. After I got over the initial excitement (although the honeymoon period still doesn't seem to have faded) I realised that I would have to find equivalents for most of the programs I'd gotten so used to using. I've compiled a list of the most useful software that I've discovered.

Firefox
This download, of course, is a complete no-brainer. Safari, which is pre-installed, is a fine browser, but it isn't very extendable, with far less plugins available. Firefox is essential for working on the web.
http://www.mozilla.com/en-US/firefox/

Adium
If like me you have a number of different IM services that you sign into on a regular basis, it can get confusing. Adium is a free IM client which combines all of your contacts in one program, everything from Gmail to MSN.
http://www.adiumx.com/

Skype
Not only can you use Skype to make free calls to anyone else with a Skype account, there are also some useful paid services you can use to save money on your phone bill, like SkypeOut, which allows you to call landlines and cellphones. The cost-per minute is usually less than your cell or landline, especially when calling overseas.
http://www.skype.com/

VLC
VLC is the ultimate in media players. Whilst its interface is very basic, it is compatible with pretty much any kind of video or audio file you can throw at it. Downloading VLC meant that I didn't have to spend hours downloading different codecs for my Mac.
http://www.videolan.org/vlc/

Handbrake
One of the better features about MacBooks is their battery-life (certainly compared to my last pc laptop, which after 2 years use was down to a 15 minute charge.) I wanted to take advantage of this by watching movies and TV shows on the go, but I didn't want to have to lug around a bunch of DVDs with me. Handbrake proved to be an excellent solution - an easy-to-use and feature-rich DVD converter.
http://handbrake.fr/

Gimp
Whilst you might have used Photoshop before, chances are that you won't immediately have a OS X copy. Gimp can be an able stand-in. It allows you to do most of the things that you could do in Photoshop. The drawback is that it isn't quite as easy to use, and you'll need to resort to complicated workarounds sometimes to achieve effects that you could easily get in Photoshop. It also requires the X11 environment to run, which means that your familiar keyboard shortcuts won't work, and you might have some trouble setting it up. It comes in two versions: normal Gimp, and Gimpshop, which looks more like Photoshop.
http://www.gimp.org/macintosh/
http://www.gimpshop.com/

Inkscape
An open-source vector graphics editor, the closest you can get to Illustrator without paying for it.
http://www.inkscape.org/

Cyberduck
This free FTP client doesn't have a huge amount of functionality, but it will get the job done, and it has a nice interface.
http://cyberduck.ch/

MindNode
If like me you find it easier to keep on top of projects visually, then MindNode is a must-download. It's a mindmapping program and simple as it is, it works like a charm and it looks beautiful. There's a paid version called MindNode Pro which is more advanced, but MindNode itself is fully-functional.
http://www.mindnode.com/

NeoOffice
If you didn't invest in a copy of iWork or Office for Mac, you'll be fairly stuck for normal word-processing or spreadsheeting. That's where NeoOffice comes into play. NeoOffice is a port of the popular open-source OpenOffice suite of programs. It includes word-processing, spreadsheet, presentation, drawing and database programs. A major bonus is that it supports many formats, so you'll be able to read all your old files.
http://www.neooffice.org/

JDarkRoom
It took me a while to find this, a free cross-platform version of one of my favourite programs of all time. JDarkRoom is an application that emulates 1980s style word-processing: green letters on a black screen. The aim of JDarkRoom is to eliminate all distractions and allow you to concentrate on writing: just you and the words on the page.
http://www.codealchemists.com/jdarkroom/

Urban Terror
Urban Terror is the freeware game you need to get. It's an online multiplayer first person shooter based on the Quake engine, but with a focus on more realism. The best free game I've ever played, and better than most I've paid for.
http://www.urbanterror.net/page.php?6

These are just some of the many great freeware applications that are out there if you take the time to look. You should exercise caution when downloading freeware or open-source applications, because they aren't always stable, and in some cases can even be dangerous. A good site to check out is osx.usethis.com, which tells you what software other people are using, and how many, along with comments.