Yes, they do exist. Check out a really entertaining post by Amanda Claunch at the blog of the Missouri Historical Society. A taste:
In the Victorian era and into the early 20th century, it was also popular to send “vinegar valentines” to fend off unwanted suitors or to tell someone you didn’t like how you really felt. Always insulting, the cards mocked a person’s profession, personal characteristics, or appearance. To add insult to injury, the cards were designed to be anonymous and didn’t require postage, necessitating the recipient to pay for delivery.
Relatively few of these vinegar valentines survived, because the recipients frequently destroyed them. There are even accounts of these mean-spirited missives resulting in fistfights, lawsuits, and shootings! The Missouri Historical Society’s collections contain hundreds of valentines, and among the cards covered in hearts, lacy cut-outs, and sentimental poetry, there are also some zingers.
Read the entire piece and see the anti-Valentines here.