My understanding is that strict paleo does not include dairy. Not everyone here is eating a strict paleo diet. Personally, I eat full fat yogurt and aged raw milk cheese. I try to make sure all my dairy is from grass fed cows.
If you're having any sort of digestive problems or inflammation issues, it's probably worth giving up all dairy for a time to see if it helps, otherwise, it's a personal decision.
Yogurt - Not really Paleo in the classic sense.
Plenty of folks eat it, from the "Swedish Paleo" vibe (Paleo + Dairy) to the Primal Blueprint (mostly centered around lower carb dairy), to the Weston A. Price vibe - which is raw, fermented/cultured dairy. I eat raw, hard cheese with low lactose because I have some gut issues myself.
It is a post-agricultural food, and that pretty much takes it out of realm of "Paleo" but not necessarily out of the realm of "Ancestral". But what you have to ask yourself, "is this food going to help me with my goals?"
Confused yet? Basic summary below:
If you came to paleo to solve gut issues - I'd suggest skipping any dairy initially, reintroducing cheese and heavy cream before introducing yogurt (yogurt does have a teensy bit of lactose even the good, raw milk, full fat yogurts).
If you came to paleo to lose weight - dairy may help you or hurt you (depending on gut health and binge tendencies) - I'd try full fat yogurt (don't swim in it though) and cheese.
If you came to paleo to improve athletic performance (and have no existing issues) - then you have some leeway in eating dairy.
Dairy is more Primal or WAFP. Raw is better than pasturized (probiotics) but it's not available everywhere. There are many people who are lactose intolerant or have problems with casein and so stay away from dairy. I eat goat milk products because I can digest it better than cow's milk and because it helps me get in needed protein that I can't get elsewhere.