I've mostly done intranet development and never worried about accessibility features. For a public website, is there certain types of sites or data where specific accessibility features are legally required? Or is it always just my decision based upon my targeted demographic?
As others have mentioned, legislation on the matter depends on your local laws, though generally speaking there will be a legal requirement for government sites if you are in the US or Europe.
If your site is a web application might ever be of interest to large organisations like a bank, then they will probably insist on conformance with the WCAG standards - our clients certainly insist on this for all internal and external bespoke work (and it is a deciding factor if choosing between external off-the-shelf solutions).
Legal and contractual issues aside: if you do, or plan to do, web design or web programming for hire I recommend making all your work accessible where possible and downgrade gracefully when not - that way your future portfolio has greater chance of looking impressive to clients who know about such things. And remember that there is more to accessibility than just making it browsable by the blind using screen readers, and even then try not to assume what people will want to browse - a user that has been blind since birth might still find something of interest in a good art gallery site as it will no doubt contain interesting facts about the pieces, artists and places & people depicted.
Of course "just my decision based upon my targeted demographic" is how most sites seem to be run in this area, including some of my output if I'm completely honest!
If you are developing a site for the government then (depending on your country) there will probably be mandatory requirements that you implement such features. But there is also legislation that covers all websites, for example in the UK there's the Disability Discrimination Act (DDA):
Section III of the DDA, which refers to accessible websites, came into force on 1st October 1999 and the Code of Practice for this section of the DDA was published on 27th May 2002.
According to this page in the US there are no laws concerning website accessibility for non-government websites.
In the United States, there are no laws binding business to conform to any level of website accessibility. Many government and government-supported organizations are bound by Section 508 of the Rehabilitation Act Amendments of 1998, but these rules do not extend to private business concerns.
I don't think "required" should be something you see as being optional. Every site should be as accessible as possible. The very next sentence in the above quote is:
However, even if you conduct business only in the United States, this is little reason to fail to conform to common website accessibility standards found in the WCAG 2.0.
Wikipedia had a great way of saying it (emphasis mine):
When sites are correctly designed, developed and edited, all users can have equal access to information and functionality.
This is essentially a legal question and you should ask a lawyer if you want an authoritative answer on what your local laws say on the matter.
Accessibility laws are however rarely enforced (especially against non-governmental sites) and you are more likely to catch flak from special interest groups over a lack of accessibility than any legal trouble. If you are designing a site where the user are somewhat captive (i.e. have no viable online alternative or it is difficult/expensive to move to an alternative) then you should most definitely view accessibility as a major concern. If your users can easily choose alternatives, then you need only worry about lost traffic.