What do we mean by Accessibility?
From the Oxford English Dictionary
Able to be reached or entered.
Stop and think about that for a second. Making your site accessible includes:
  • Making sure people using Mozilla or Safari can read it.
  • Making sure Search Engines index your content and present your site well.
  • Making sure people with a slow connection speed don't give up waiting.
  • Making sure people with a disability like color blindness can read your page.
  • Making sure that even if someone has something slightly different about how they're browsing (javascript turned off, perhaps using a screenreader, even just using a mobile phone or PDA,) they can still access the information you provide.

Accessibility is about making sure you're in touch with your users.

Who Cares?
If you have a website, why did you create it?
Was it to sell your business on the web? Then having more people able to access your site makes commercial sense, particularly as they may turn into sales.
Present information on a hobby? Well perhaps people using anything other than Microsoft's latest browser would like to read about it too.
Or is it a family site, to tell people about what you do in your life? Other people may take pleasure in reading it too.
Whatever the reason, there are few (if any) sites that wouldn't benefit from being accessible to more people.

More info: http://www.webnauts.net/accessibility.html

How do I make my site accessible?
This is the full W3C Checklist of things you can do to make your site accessible.
Note they are divided into priorities, 1 being things you must do to make your site accessible, 2 being things you should do, and 3 being things that would make your site seriously accessible.

If that link looks too complicated for your liking, try the W3C's quicktips.
From http://www.w3.org/WAI/References/QuickTips/
  • Images & animations: Use the alt attribute to describe the function of each visual.
  • Image maps. Use the client-side map and text for hotspots.
  • Multimedia. Provide captioning and transcripts of audio, and descriptions of video.
  • Hypertext links. Use text that makes sense when read out of context. For example, avoid "click here."
  • Page organization. Use headings, lists, and consistent structure. Use CSS for layout and style where possible.
  • Graphs & charts. Summarize or use the longdesc attribute.
  • Scripts, applets, & plug-ins. Provide alternative content in case active features are inaccessible or unsupported.
  • Frames. Use the noframes element and meaningful titles.
  • Tables. Make line-by-line reading sensible. Summarize.
  • Check your work. Validate. Use tools, checklist, and guidelines at http://www.w3.org/TR/WCAG
Looking for more information? Read the other stickies in this forum, or just ask a question!

I hope this helps anyone who's simply looking to find out about web accessibility reasonably painlessly!