Now that political incorrectness is less tolerated, I hear fewer and fewer of the derogatory words like dago. But I think something else is in play too: immigrants of past European generations who are now assimilated are no longer as likely to be labeled. They blend in well and are not as easily identified. So dagos, wops, polacks, micks, frogs (though I'm not sure that was commonly used in the U.S.), kikes, yids, and similar words are not used as often.
Blacks, though most have been here much longer than some of the European immigrant groups, are still visibly identifiable, as are Asians, some Hispanics, and more recently Middle Easterners, especially those who wear identifiable traditional "trademarks". I still hear some of those derogatory words.
Derogatory words are used for WASPs too, of course. It seems like every group can find some way to label "the other" in a condescending or unfavorable way. Us against Them seems to be a human characteristic.
I haven't studied this - just an impression. I'd be interested in what others think.