Sometimes one of my friends switches from Linux or Windows to OS X, and asks me for tips on software. If an app makes it to this page, I both like it, and personally use it often.

Geeky/Utility

Alfred
Application launcher, and much else besides. If you like doing things quickly from the keyboard, rather than clicking around with a mouse, Alfred is your friend.
Transmit
FTP client with a nice interface and lots of features.
Cyberduck
If Transmit doesn’t do it for you, try floating a Cyberduck. Cyberduck is an alternative, open source FTP client with some interesting differences from Transmit, including better Amazon S3/Cloudfront support.
DaisyDisk
Gorgeous disk usage viewer.
Virtual Box
Free, open source virtual machine software. Run Windows or Linux in a virtual machine on your OS X desktop.
Super Duper
Disk cloner.
iStat Menus
Put CPU, disk, network and other meters right in your menubar.
Hazel
Keep your Mac tidy and organised, without doing it all yourself. Hazel will organise your desktop, file downloads into the right places, even zip things up and set their Spotlight info. Excellent for automating stuff.
TextExpander
Type pre-prepared chunks of text using keywords. I use this for email, so I can just type “myplace” and TextExpander inserts my address and a link to Google Maps, say. Save your fingers!

Multimedia

Airfoil
If you have an Airport Express with iTunes, or more than one Mac, try Airfoil. Send any audio to your remote speakers, use another Mac as a remote speaker, play video with the soundtrack synced perfectly on your remote speakers.
Permute
Video and audio format converter with an easy, drag-and-drop interface.
Fission
Simple, lossless audio file editor. Copy, paste, trim and split audio, and you can do it without losing quality in compressed files. It’s no Audacity, but sometimes, that’s a good thing.

Graphics

Pixelmator
Lovely little image editor for you day-to-day raster graphic editing needs. Prettier and less annoying than an Adobe product. Not that that’s hard.
Acorn
If you don’t get along with Pixelmator, Acorn is another image editor you might want to try. I tend to swap between both, depending on exactly what I’m doing. They’re both good.
Sketch
Lovely vector graphics editor. This is what I used to replace the hole in my life left by Freeverse’s sad abandonment of Lifeform. Version 2 of Sketch looks even more interesting, and I’m very much looking forward to seeing it.

Web Design

Coda
If you hand-craft your websites, you can’t do better than Coda. Truly beautiful code and CSS editor, with ftp, shell and reference books built in.
CodeKit
Web development utility that does all sorts of handy things. Image compression, script minification, LESS compilation, auto-refresh of browsers when files change… All sorts of goodies.
Color Schemer Studio
Colour scheme designer. Can do funky things like create a colour scheme from a photo you provide. Excellent way of making lovely colour schemes for your websites.

Writing

Scrivener
Outlining, research and writing tool. I use this for drafing web content, articles and fiction. If you write, give it a try.
Byword
My favourite minimal writing environment with good built-in Markdown support.

Games

Oolite
Open source Elite clone, with spookily identical playability to the original.

Blogging and Social Networking

MarsEdit
I’m typing these very words in MarsEdit. It’s a Blogging client for multiple platforms, including WordPress and Movable Type.

RSS and Reading Later

NetNewsWire
RSS newsreader that can sync with other Macs and the web-based NewsGator service. There’s also a Windows client, FeedDemon. Both clients are available free; the web service needs a subscription.
Pocket
“Read this long thing later” service. Did someone tweet a link to a long and interesting article you don’t have time for right now? Send it to Pocket and have it presented later, when you fire up their well-designed web interface, or Mac, Windows, iOS or Android clients.
I switched from Instapaper to Pocket during the short period when Instapaper was languishing, somewhat under-developed, just before Marco sold it. I’d definitely check out Instapaper too, if I were you. The new owners look to be doing great things.

Productivity

Fantastical
Great natural language calendar entry. That is, hit the little menubar icon, and type something like “Lunch with Judy at Renatos 9pm Friday next week”, and it’ll turn that into a calendar entry for “Lunch with Judy”, location “Renatos”, for 9pm on Friday next week. No fiddling with iCal’s annoying editing system, and you can set defaults for meeting lengths, alarms, and so on.
Omnifocus
I’ve tried a lot of Getting Things Done apps for the Mac (plus several web-based ones.) OmniFocus from the Omni Group is definitely my favourite. There are companion iPhone and iPad apps. It’s pricey, but there’s a free trial, and if you’re into GTD, you know a good tool will save you money in the long run.