Disinterested traditionally means having no stake in the matter. For example, when you are arguing with someone, you might bring in a disinterested third person to help settle the issue fairly. Uninterested traditionally means not engaged, bored, or unconcerned.
Many careful writers still observe the distinction between the words, and doing so is never wrong (and is probably the safer choice in more formal writing). But the reality is that disinterested has encroached on uninterested‘s territory and is now frequently used to mean not engaged, etc. This is understandable considering that the prefixes dis- and un- both mean not and that the traditional disinterested draws on a little-used sense of interested (i.e., having a stake in a given matter), but the change is also a little unfortunate because disinterested can be a useful word. We can do without it if we must, though, as it has many synonyms, including impartial, neutral, unbiased, and objective, that can work in its place.
Disinterested is commonly used where uninterested would traditionally make more sense—for example:
Tens of thousands of volunteers, many of whom had been disinterested for much of the year, turned up at campaign offices over the weekend. [Guardian]
Ask any teens about their parents’ jobs and you’re bound to get some shrugged shoulders and thoroughly disinterested looks. [NBC News]
Fox Sports is convinced it can convert those AFL and NRL fans disinterested in cricket to continue their subscriptions over summer. [The Age]
But the change is not fully engrained, and the distinction between the two words is still sometimes observed—for example:
They are not uninterested in jobs and the economy, but they give the biggest cheers for same-sex marriage and ”don’t ask don’t tell”. [Sydney Morning Herald]
[His] numerous and mighty benefactions are seldom used to support an image of him as a model of disinterested philanthropy. [New York Times]
A scholar should read all the perspectives with as much detailed knowledge as can be mustered … and make every attempt to be disinterested. [Sinning in the Hebrew Bible, Alan F. Segal (2012)]
The Wall Street Journal reports that a whopping 59% of female respondents aged 16 to 19 said they were uninterested in or averse to sex. [Huffington Post]
We must admit, however, that we had trouble finding even a few examples of disinterested used in its old sense in 21st-century writing. Those who resist change to English might have to accept defeat on this one.