This is a very comprehensive list of astro software compiled by Pierpaolo Ricci. All free to download, but some are shareware, trial/demo type as well. He keeps it pretty up to date, adding 15 or 20 every few months.
I noted some omissions of some software I find useful and have contacted him for inclusion next update.
(Updated 8 May 2014)
Thought I'd post here a much more compact list of astro software that I regularly use (marked *), and maybe if you post your recommended ones too we can make this a one-stop-shop to help others. Trying to keep it a list of free or very cheap software for those just starting out, figuring by the time you're ready to really fork out for some of the more expensive software you pretty much know what you want my then anyway.
All software below is free unless noted otherwise. I've tried to keep them grouped, but not easy as some software overlaps categories handling several things. In this case I put them in the heading I think most apt.
*CCD Calculator (Win)
*Astroplanner (Win/Mac) US$45 as at 08/05/14
Alignmaster(Win) EU$14 as at 08/05/14 - a negligible price to pay considering the hours and hours it will save you doing time-consuming drift alignment. Get polar aligned in minutes, if not seconds. Note that I no longer use this regularly. I have been using OpenPHD's drift align feature as per below.
*PHD2 (OpenPHD) (Win/Mac) - the next generation of Craig Stark's PHD (see Guiding Software below). Has new features, one of which is a useful drift align tool.
EQAlign - see link below under guiding software. Can do polar alignment as well.
*PHD2 (OpenPHD) (Win/Mac) - the next generation of Craig Stark's PHD (see PHD below). Has new features and enhancements.
PHD Guiding (Win/Mac) - by far the most popular guiding software around.
Metaguide(Win) - not just for guiding, can also be used as a powerful collimation aid
*Cartes du Ciel (Win/Mac/Linux)
Jupiter 2.0 (Win) - for Jupiter moon positions
Virtual Moon Atlas (Win)
Orbitron (Win) - satellite tracking software
Where is M13? (Win) - kinda different. It's actually a 3d view of our galaxy, the Milky Way. You can put in a Messier or NGC object and it'll show where it is in relation to where our Solar System.
*Sequence Generator Pro (Win) US$99 as at 08/05/14- reasonable price, very powerful and useful.
Nebulosity (Win/Mac) US$60 as at 23/10/09 - quite powerful, does image capture, stacking, and post-processing. Can also link to PHD Guiding to drizzle.
Astro Photography Tool (Win) free demo, EU$12.70 as at 6/8/10 - if you're imaging with a Canon DSLR, and if you're reading this you probably are, this one is definitely worth a look.
K3CCDTools (Win) US$49 as at 23/10/09 - more for webcam and planetary/lunar imaging, but can also drift align
Craterlet(Win/Mac) - also more for webcam and planetary/lunar imaging.
Deep Sky Image Processing:
*PixInsight (Win/Mac/Linux) EU$199 (excl VAT) - extremely powerful, specifically written for astro image processing although can be used on normal photos. Be warned, there is a steep learning curve, as the philosophy of image processing using PI is different to PhotoShop that you're probably used to. That being said, in my opinion, PI is the ultimate for astro images, and it's cheaper than PS by a mile.
Troy's Astro Actions for Photoshop (Win/Mac) - check out the thread here on POTN
Noel Carboni's Astronomy Tools Photoshop Action Set (Win/Mac) US$21.95 as at 08/05/14
Deep Sky Stacker (Win)
Planetary Image Processing:
Star Tracer - fill in the gaps on your star trail shots, or even extend them (Win) US$35 as at 08/05/14