I hate this phrase. Not because I have a problem with it per se, but because people always use it wrong. They read it in some article, decided to use it themselves, and even though they know what it means, they use it incorrectly.

The likes of introduces a comparison. You wish to describe a set of elements by exemplifying a couple of them. It's exactly like a mathematical series. Do you remember those problems from school?

1, 4, 9, ...

The first three numbers describe this series uniquely, it can only have one possible solution. The solution for a_n is n². That is, if you apply the formula n² for every n, then you get

1², 2², 3², 4², 5², ...

equal to

1, 4, 9, 16, 25, ...

and hence the series is solved.

And this is exactly what the likes of means as well. It defines a set more or less uniquely (without mathematical rigor, of course), so that the set does not have to be stated in its entirety. So what's the problem? There are two ways in which this phrased is misused.

Stating the full set