So... You've got yourself a fancy new PC... Or maybe just an old one... Or even better, you got an Apple.
Now you want it to do something. You're going to need software. You can always go throw your money away on "Industry Leading Brand Names", OR... you could use Free/Open Source Software (F/OSS) and save your greenbacks for your kid's college education (they'll no doubt be as smart as you).
Having said that, I'll provide a list of software I like.
But first, one more note... as most people realize... web-based software probably is the future. Many 'applications' you never download/install, but simply visit their website. As such, below are both links to traditional software, and web apps!
Don't ask me what is current, find out yourself: http://www.google.com/search?q=best+web+based+applications
http://www.google.com/intl/en/about/products/index.html - Google is a juggernaut, they have lots of stuff (Including the powerful Google Docs).
http://windows.microsoft.com/en-us/windows/products - Microsoft is trying to do the same thing as Google, did you know they have Word/Excel 'online' (if you have an MSN account).
Lots more below...
http://ninite.com/ - This is pretty cool... you check off the software you want, it automates the downloads and installs. TIME SAVER!
Many of the individual packages referenced below are included in NiNite too..
http://www.apple.com/mac/app-store/ - taking a cue from their iOS devices, for Macs there is a pretty easy place to get software, AND keep it updated!
http://firefox.com/ - my favorite browser to replace Internet Explorer
good extensions, I don't keep up to date on which of these are still available, but you can try them...
https://addons.mozilla.org/ - the BIG repository...
Also has a ton of extensions, and some fancy features that work with Google Docs
https://chrome.google.com/webstore/detail/adblock/gighmmpiobklfepjocnamgkkbiglidom?hl=en
http://www.opera.com/ - Another good web browser
http://www.adobe.com/reader/ - For reading PDFs (but you might want to try Foxit, go back up to the Ninite.com link)
https://github.com/microsoft/PowerToys - Windows Resizer tool, and other stuff
http://photos.google.com/ - a nice free picture manager, syncs with smartphones easily.
https://pixlr.com/editor/ - pretty clever web 2.0 editor, and get the browser plugin listed above.
http://www.gimp.org/ - Free Photoshop clone, for power users.
Online photo storage/hosting - more courteous then emailing a dozen people a dozen photos...
http://www.shutterfly.com/ - one of many sites that turns your photos into business cards, thank you notes, coffee mugs, etc.
Tiny/easy photo sharing
(Stop gap measures until you get OS X or Linux)
AntiVirus
With Windows 10, Microsoft Defender is built in / free... but often when you buy a new PC they'll layer McAfee or Symantec on top of that. Usually I uninstall anything that has a yearly subscription cost.
http://www.microsoft.com/en-us/security_essentials/default.aspx - If you still deal with Windows 7, you had to manually install Security Essentials, but still free.
http://free.avg.com/download-avg-anti-virus-free-free-edition - AVG Free AntiVirus - commercial product, free for home use, they have got a bit more obnoxious lately
http://free-av.com/ - Avira
http://www.clamwin.com/ - based on the ClamAV OSS product, completely free!
http://www.avast.com/eng/download-avast-home.html
http://housecall.trendmicro.com/ - one time / one pc checkup? Don't bother installing AV, just run it from the web.
AntiSpyware / AntiMalware
Again, Defender/MSE (above) above is pretty good
http://www.lavasoftusa.com/software/adaware/ - ADAware spyware removal
http://www.safer-networking.org/en/download/ - SpyBot Search & Destroy
Other
Check out your Startup Control panel via msconfig.exe and sane Startup folders.
...backup, backup, backup ... seriously
This used to be a harder then not task, but it's getting better/easier/cheaper every day
First off, on a personal level... what are your 'digital documents' worth to you?
For home users, this typically means: personal photo albums, school work, family trees, scanned documents, etc
For business users, you should know what your valuable data is: accounting, payroll, invoices, taxes, etc
Do NOT worry about: purchased software, commercial music & videos, etc... those can be re-acquired
Do NOT worry about email, I know you are using one of the web-based email providers above.
Secondly... for family friends, the easiest way to get started with backups, is buy a second hard disk
http://www.amazon.com/External-Hard-Drives-Storage-Add-Ons/b?ie=UTF8&node=595048 - <$100 should be plenty.
Or maybe even: http://www.amazon.com/b?ie=UTF8&node=13436301 - Network Attached Storage, then more then one PC can use it!
If you have Windows 7 use the built in backup tool with an external usb disk
For a bit more control and configuration, I've used this a few times https://www.cobiansoft.com/cobianbackup.html
If your whole house/business burns down, that external USB hard-disk probably won't work any better than your toasted computer right next to it....
Next level move... put your usb disk in a firesafe, your car, or leave it at work (but then you might also consider encrypting the data).
So, thirdly I REALLY like online backup systems, if you have an Internet connection and a reasonable amount of data
In no particular order or preference (choose what fits your needs/price best) - http://en.wikipedia.org/wiki/List_of_online_backup_services
http://www.backblaze.com/ - unlimited data for ~$99/yr
... and there are a now quite a few 'cloud storage services' that you can use for offsite backup or just general storage...
https://www.apple.com/support/icloud/storage/ - Apples extensible iCloud storage, and if you do use an iPhone, probably a no-brainer.
https://www.dropbox.com - Probably the most recognizable name in unified cloud storage
http://lifehacker.com/how-to-use-amazon-glacier-as-a-dirt-cheap-backup-solut-1460814873
(You know, music, movies, etc.)
http://handbrake.m0k.org/ - not really playback, but let's you rip DVDs to store more conveniently on your PC, iPhone, DVR, etc
http://www.filebot.net/ - Good for renaming some files... per my one of my buddies.
http://www.openoffice.org/ (and boring spreadsheets too)
https://www.lucidchart.com/ - pretty cool for Visio-like documents
Want to create PDFs?
It's built in to Mac OS X in the Print Dialog
OpenOffice, some web browsers, and other programs allow you to 'Print to file'
Or you can use these from ANY Windows program that allows printing...
http://www.pdfescape.com/ - Online PDF editing, great for signing without printing or buying Acrobat Pro
http://www.7-zip.org/ - compress/decompress pretty much any file!
http://en.wikipedia.org/wiki/Comparison_of_BitTorrent_software - Bittorrent allows you to quickly download files from the Internet
A good light weight install-less Windows client: http://www.utorrent.com/
Disk Space accounting
http://www.nirsoft.net/utils/folrep.html - a 'decent' way to figure out which folders are eating up disk space, like Unix 'du'
http://www.uderzo.it/main_products/space_sniffer/ - For PC. Cool visual space accounting tool
http://grandperspectiv.sourceforge.net/ - For Mac, it took me a second, but after that I liked the highlighting of the parent folder/box
http://www.derlien.com/ - Form Mac, Disk Inventory X, more bells&whistles then GP, but seems a bit slower... still good!
http://www.corecode.at/smartreporter/ - SMART status... it might tell you if your disk is about to die
https://www.belarc.com/products_belarc_advisor ... pull a nice inventory of what's in your Windows computer.
https://www.forensit.com/downloads.html - Windows profile mover
http://www.ragingmenace.com/software/menumeters/#download - little bitty meters for your mac, so you can keep an eye on cpu/disk/network ... pretty geeky cool... not to mention free/GPL
https://seriousbit.com/netbalancer/ - A Freemium bandwidth monitor for Windows, including rate limiting by process!
https://join.me/ - A pretty cool desktop sharing app, now owned by LogMeIn actually... nothing to install for the viewer... handy.
http://www.freesmug.org/portableapps - put your favorite programs on portable storage, good for when you use friends Macs!
http://www.opensourcemac.org/ - lots of overlap with my page, but nice to see others have the same idea!
Library stuff, I like the idea of books on computers
http://www.gutenberg.org/ - public domain ('classics') books digitized
http://www.delicious-monster.com/ - neato Mac media library cataloger
http://earth.google.com/ ... Google has gone mostly web based for Earth, but still can download Pro version.
https://www.duckdns.org/ - Dynamic DNS client ... 'free forever' ... unlike some of the old popular ones...
http://www.noip.com/ - These guys aren't too bad, send you monthly 'checkup' emails
http://www.makeuseof.com/tag/5-best-dynamic-dns-providers-can-lookup-free-today/
http://www.tuxpaint.org/ - now if only KidPix ( http://www.mackiev.com/kid_pix.html ) was F/OSS
http://www.poissonrouge.com/ - a French/English website... pretty creative
http://www.starfall.com/ - a phonetic reading site
If you aren't absolutely in love with Micro$oft Windoze... Mac OS X is better, Linux is FREE and pretty easy to install (or sometimes even run from just a CD).
http://www.apple.com/macosx/ , you'll need a Macintosh of course (Much of the software above is of course Mac-friendly)
http://knoppix.org/ - Boot linux from a CD (or DVD), neato.
https://tails.boum.org/ - for the ummm, security conscious
http://www.puppylinux.org/ - a really lightweight linux, good for ridiculously old PCs
https://dban.org/ - clean those old PCs up too
Also, don't feel trapped into your current OS, run another PC inside your existing one!
http://www.vmware.com/ - current leader in virtualization, run a PC on your mac!
http://www.virtualbox.org/ - not as popular as VMware, but OSS and free!
http://www.parallels.com/ - a Vmware competitor