I'm using 4 break points but as ralph.m said each site is unique. You should experiment. There are no magic breakpoints due to so many devices, screens, and resolutions.
Here is what I use as a template. I'm checking the website for each breakpoint on different mobile devices and updating CSS for each element (ul, div, etc.) not displaying correctly for that breakpoint.
So far that was working on multiple responsive websites I've made.
/* SMARTPHONES PORTRAIT */
@media only screen and (min-width: 300px) {
}
/* SMARTPHONES LANDSCAPE */
@media only screen and (min-width: 480px) {
}
/* TABLETS PORTRAIT */
@media only screen and (min-width: 768px) {
}
/* TABLET LANDSCAPE / DESKTOP */
@media only screen and (min-width: 1024px) {
}
UPDATE
As per September 2015, I'm using a better one. I find out that these media queries breakpoints match many more devices and desktop screen resolutions.
Having all CSS for desktop on style.css
All media queries on responsive.css: all CSS for responsive menu + media break points
@media only screen and (min-width: 320px) and (max-width: 479px){ ... }
@media only screen and (min-width: 480px) and (max-width: 767px){ ... }
@media only screen and (min-width: 768px) and (max-width: 991px){ ... }
@media only screen and (min-width: 992px){ ... }
Update 2019: As per Hugo comment below, I removed max-width 1999px because of the new very wide screens.