This list are the applications that most use in CSE. We try to focus on applications that are free, inexpensive and open source. If such applications don't exist, we list the best piece of software in that category. If you want a specific piece of software, try MacUpdate and VersionTracker. You can also send your question to the mailing list.
TextMate is a brilliant general purpose text editor while others prefer BBEdit. SubEthaEdit is a novel collaborative text editor that some use.
If you can't afford the above, TextWrangler is a mini-BBedit that's good. Vi users can try Vim and Emacs users can try Carbon Emacs.
As far as IDE's go, Xcode and Eclipse are good and free options.
For creating Tex documents, try TextMate or TexShop. If you need to embed equations in documents, LaTeXiT is your best option.
For creating posters, graphs and other vector based images, OmniGraffle is the standard but is expensive. For more free form work, try Inkscape, which is an Illustrator clone.
NeoOffice is a Mac friendly version of the free OpenOffice. You can use your site or personal license for Office 2004. Apple also has Keynote for presentations and Pages which may or may not come with your machine.
Note taking can be done with Mori, Yojimbo, OmniOutliner. For quick and free notes try, Notepad Widget or your favorite text editor.
Camino is based on the Mozilla rendering engine, but unlike Firefox it is "Mac-y" in nature. It uses Keychain, OS X elements, etc. You can find optimized versions on MozillaZine and extensions at PimpMyCamino.
Safari is the standard OS X browser. WebKit is Apple's open source (and often faster) browser engine. Find extensions at PimpMySafari.
Firefox, is a cross-platform browser, but there are processor optimized versions available. Find extensions at Mozilla AddOns.
Most people use Adium (based on Gaim but pretty) because it's customizable and allows for all the chat protocols in one client. It has medicore file transfer support so some prefer iChat paired with Chax.
For VoIP, Skype and GizmoProject have Mac clients. For those still on IRC, try Colloquy.
You can use Mail, Thunderbird or Entourage. Mail tends to be more popular because it's easy and simple. Entourage tends to be the reverse of Mail, and Thunderbird sits in the middle. If you use Mail, try SpamSieve or it's free counterpart JunkMatcher for better filtering. Use LetterBox to get three column layouts.
You can use iCal or Entourage. iCal tends to be more popular because it's easy and simple. Entourage tends to be the reverse of iCal but has better Exchange server support.
Vienna is an open-source client that works well. NetNewsWire (both pro and lite) are pretty good too.
PDFView is vastly superior to Apple's Preview. Also, take a look at yep which is like iPhoto for your documents.
For FTP/SFTP, Cyberduck and Fugu are nice and free, while Transmit is nicer and not free. Fetch works and is free for students.
For torrents, try Azureus if you need lots of functionality and plugs-ins. For more Mac-centric clients, Tomato Torrent, Transmission and XTorrent are all brilliant.
For general downloading, there is Speed Download which is elegant and iGetter which works.
For listening to music, iTunes is the standard and you can get some useful scripts. There are also Media Rage or IEatBrainz (old) for tag management, Corripio or Amazon Album Art widget for artwork management. If you switch music libraries often, try Libra.
For making music, Garageband is pretty good if you don't want any "pro" apps. Audio editing can be done with either Amadeus or SoundStudio. You can also try Audacity.
As far as playing video, QuickTime paired with Perian and Flip4Mac is a really powerful combination. You can also use VLC, or MPlayer.
For making videos, you can pick your choice of iMovie HD, Final Cut Express HD, and Final Cut Studio. Which one you pick depends on what you want to do (and spend).
OS X has built-in disk burning, but most find Toast much better. Burn is a free alternative.
iPhoto which is simple and Photoshop which is complex are at the two ends of the spectrum. You can also try GraphicConverter which sits neatly in the middle, or Gimp.app.
It's hard to explain these apps, but they sit between using a command line and using a gui. LaunchBar gets you instant access to apps, documents, search engines, etc. It's extremely quick, stable and has limited features. Quicksilver is a similar open source application, but with slightly less stability and a ton more features.
Growl is allows applications that support Growl to send you notifications. A lot of applications use Growl and it's generally a useful thing to have installed.
SuperDuper makes a bootable image of your hard drive. Chronosync makes versioned incremental backups of any folder you specify.
OnyX helps you run system maintenance tasks and configure hidden parameters. AppleJack is a similar utility which runs in single user mode.
Intel Users should try CoRD and PowerPC users should try Microsoft RDC. You can also install rdesktop in darwinports or fink.
Chicken of the VNC is the standard VNC client and there is also a nice NX client.
You can try virtualization (Parallels, VMWare), natiive install (BootCamp) or a hybrid (CrossOver). If you do a lot of hardware or graphics intensive work, you want to use Windows natively. If you need a full fledged Windows install try virtualization. If you only have one app and it's supported by Crossover, then use that.
If you want know the differences, try this Guide for Choosing Boot Camp or Parallels to Run Windows on an Apple MacBook