TexShop. I write mostly in LaTeX. In the past I used LaTeX only for research but now I make almost all my handouts and discussion documents in LaTeX. (When I don't, they are almost always InDesign one- or two-page documents.) I know that there are WYSIWYG environments for people who want to write in a Word-like environment, but being a long-time programmer I prefer to edit LaTeX source code.
R. This is my main programming environment, having replaced Stata and MATLAB. I considered using Octave or Python, but in the end R is the best combination for my needs.
Mathematica. Every so often I need to do some tedious calculus, so I trust Mathematica for that. (When I do more than a few pages of calculus by hand, there's usually a missing sign or a transposed fraction somewhere.)
TextWrangler. Heir to the venerable BBEditLite, it's my mainstay text editor. I use it for all text that is not LaTeX, including programming, web posts, drafts of long emails, and outliner for talks. (I don't use a specialized outliner program for the reasons I gave in this post.)
Keynote. I used it as mostly a projector management system, with all content created on other tools, but now I use it for about one-quarter to one-third of all slides. Integration with iTouch and iPad allows for good control (which, I'm told, has existed in the Windoze ecosystem for several years now…).
Numbers. Not as good as Excel for most tasks that a manager would use a spreadsheet, but it's a simple way to mock-up quick models for class demonstrations. Anyone doing serious spreadsheet work must use Excel, though, since Apple seems intent on leaving the professionals behind. Really.
Pages. Although I don't use Microsoft Word as a text editor, I occasionally work with people who do. It's hard to believe that a word processor in 2015 doesn't allow facing pages (odd/even pages); were I to use a word processor rather than LaTeX, this would mean Word, not Pages. Apparently Apple is intent on leaving even school reports to Microsoft...
Adobe Illustrator. My main drawing program, for diagrams and illustrations. Even though there are now some minimally acceptable drawing tools in Keynote, they are still very weak compared to Illustrator.
Adobe InDesign. When I need to make diagrams that include a lot of text and not a lot of drawing, I prefer InDesign to Illustrator. InDesign is also my program of choice for making compact handouts, of the type I send for remote discussions or distribute at speaking events. (In the old days, I used to make my teaching handouts with InDesign, but once I went for long handouts, I switched to LaTeX.)
Adobe Photoshop. I use it for final production on many slides, though a little less now as I move towards a simpler aesthetic. It also serves as my photo editor, not that I edit photos that often.
LaTexIt. Quick LaTeX rendering for inclusion in diagrams or slides.
Voila. Page capture on steroids; can capture entire web pages as well. It has some minor editing affordances, but I do all image editing in Photoshop.
Screenflow. Captures screen, mic, and camera, for webinar-style videos. I use it for all sorts of video editing as well. Haven't opened iMovie since I got Screenflow.
VLC. Because Apple's video players are terrible.
NetNewsWire. My RSS feed reader. I could move to the cloud, and have considered that, but for now I'm happy with this. I only open it once a day, in the morning, to get a sense of what's going on.
Google Chrome. It's less of a background hog than Safari, which isn't saying much, really.
Skype. To communicate with people. Despite Microsoft's best efforts to make it unusable, the network I have on Skype is still strong enough for me to use it.
Kindle app. I have lots of Kindle books, so this is a no-brainer. (I replaced a lot of paper books with Kindle books in the 2013 declutter, using the rule that if I was likely to reread a book and its Kindle price was low, I'd rather have the electronic copy and the free physical space.)
iBooks. I also have a lot of ePubs and even some Apple iBooks, so this is again a no-brainer. I think iBooks manages multimedia content better than the Kindle.
iBooks Author. Maybe. I'm considering using this to release an interactive version of some of my teaching materials, but the limited platform (Apple only ecosystem) and the volatility of the eLearning technologies are a concern.
Simple comic. It reads comic book formats, of course, but also some other formats such as 7z which can be useful under certain circumstances. Also, I have a number of old comics in .cbr format, for nostalgia sake.
iTunes. For now my music player; it's acceptable when fed through a quality DAC. Its strong point is organization, thought that's just relative to competitors: as far as art music is concerned, no program works well, just passably.
iPhoto, soon to be replaced with Photos. To organize photos, not really a serious competitor to Photoshop when it comes to edit them.
That's it. No Handbrake for a new laptop since they no longer have optical drives (though I might install it for video file conversion, which it does very well); no email program, since I use web interfaces to keep email checking to a minimum; and no games, since I have the three I play on my phone, iTouch, and iPad (falling tiles, mahjong, and solitaire).