adv. as for example: 'great dramatists like Sophocles and Shakespeare' — Webster's New World College Dictionary's (sixth definition)
prep. such as; for example: 'saved things like old newspapers and pieces of string' — American Heritage Dictionary (fifth definition)
There's a cold war going on between me and another copy editor at my freelance job, although she doesn't realize it. Every time I copy edit a document that contains the this usage of "like," I leave it as is. But if she's the final proofreader, she changes each of these "likes" to "such as."
The reason? Traditionalists say that "like" means "similar to" — not "for example." So if you say that dramatists are like Sophocles, you're not saying he is one. You're saying that, though dramatists and Sophocles are similar, they are not the same animal. And indeed, if you're only reading the first four or five dictionary definitions of "like," you would reasonably conclude as much.
But if you read all the definitions of "like," you'll see that it's also a synonym for "such as." You could make a good case for preferring "such as." But you can't say that one is right and the other wrong.
Period. Done. End of discussion.
But for me, the fun part comes before we even read the definitions. That little "adv." before the Webster's definition and the "prep." before American Heritage delight me to no end. I just love it when dictionaries can't decide what part of speech a word is. It's all the more reason why Joe and Jane Doe should not feel bad about their grammar skills.