There are a huge number of free tools out there to help you build your site. Some of the ones I've included can be used online, others downloaded.
Luckily for anyone trying to learn web design (and even for people who have been at it a long time), there are absolutely tons of free tools to make the job easier. These are a few of my favorites.
Cross Browser Testing
Why just see a picture of how your site will look in another operating system or browser when you can get the chance to test it fully! The benefit of testing your website for cross browser / OS compatibility at CrossBrowserTesting.com is not only is it totally free for 5 minutes at a time, they give you far more than just a screenshot! You get full administrative access to the operating system, which means that if you need to test beyond a simple browser, you can load whatever applications you need. When you finish, the entire session is cleared so there's no worries about privacy.
Now that websites are becoming more and more interactive, and many web sites becoming more like full fledged applications, this handy service finally gives website developers the chance to make sure everything works well for everyone. If you need more than 5 minute intervals, their pay as you go pricing is very reasonable and does not lock you into a subscription.
WannaBrowser
The handiest online tool I've seen so far to test what your page shows to different User Agents and the exact header responses and can even follow redirects. "Why would you need that?" you ask.. Well one example is if you are blocking certain User Agents (spam bots, problematic visitors etc.) from your site, this is a fast and easy way to test that they indeed are getting a 403 forbidden error. It's also very helpful to find out if you are accidently blocking something you may not want to be.
FavIcon from Pics
Like the name says, you can within seconds create a favicon from any image on your computer with this free online tool. They even can create an animated favicon for you!
Online Image Optimizer
Quickly and easily reduces the file size of gifs, animated gifs, jpgs, and pngs. You can either upload an image from your hard drive or optimize one already online.
What The Font
Need to know what font is used in an image? Upload the file to What The Font and it'll tell you the closest match in it's database!
ASCII Character and HTML Symbol Codes
Can't remember how to make a ©, ™ or ®? Lots of symbols and non-english letters can only be written with these codes, this handy chart makes it easy to find the one you need.
Favelets
Another time saver! The tools are used just like your favorites / bookmarks. Change your resolution, validate your page and more with a just a click. If you like these Search Google for Favelets or Bookmarklets. There are a ton, and they're free and work across multiple operating systems!
FileZilla FTP
This popular FTP program is now available for multiple platforms including Windows, Mac OS X and Linux! Some of it's features are support for FTP, FTPS and SFTP, as well as the ability to resume large transfers and the option to set speed limits.
Crimson Editor - Windows Text Editor
This free text editor for Windows shows syntax highlighting, lets you edit multiple documents, multi-level undo / redo, search and replace and a lot more. Very nice for a freeware program!
Free Link Checker
Don't let the old freeware look fool you, Xenu's Link Sleuth is one of the handiest tools I use. It can check every link on your site, even exclude the ones you don't want checked and sends back an easy to read report. Runs on Microsoft Windows 95/98/ME/NT/2000/XP.
Cyberduck FTP
If you're a new switcher this is a bit confusing at first since there's only 1 window showing the websites files, not the usual 2 column view that I was used to (just drag the files in from finder into Cyberducks window). Once I got past that and figured it out I found it to be a great FTP program. It's totally free and open source, has a ton of security features (passwords are stored securely inside keychain and it's capable of SSH Secure File Transfer).
TextWrangler
TextWrangler's a very powerful text editor that's totally free, created by Bare Bones Software. TextWrangler is sort of like a little brother to BBedit but don't underestimate it.. this free text editor packs a huge punch! This freeware editor has been around (and updated frequently) for years and has proven itself to be one of the best for Mac users. Simple to get used to and it has lots of features that both new and experienced web developers and coders will love.