I came across fresh dates today at the market...

Variously, fill with cream cheese, mascarpone, nuts (pecan, walnut, almond).
Probably good also with some things that contrast with the sweetness...maybe olives, parmesan, blue cheese.
Serve with medium dry whites, like riesling or gewurtz.

@Stephanie, do you mean "not dried" ripe dates? If so, I've eaten them raw, much like an apple/pear. Some of them can be astringent, depending on how ripe they are. But I'm told, by the Persian grocer who sells them in my area, that a lot of people like this slight astringency.

Are they similar to an unripe persimmon in astringency?

Here's some more info on comparing fresh & dried dates
http://www.livestrong.com/article/527815-fresh-dates-vs-dried-dates/

Just eat them! If they aren't quite ripe and you want to serve them all at once, put them in the freezer for a bit. They soften and sweeten when they thaw.

I have been on a medjool date binge lately and can't stop making variations of these chocolate date power balls! They look & taste like chocolate truffles and are healthy!

Here are some recipes I used as a guideline in the beginning before changing it up to suit my own tastes:
https://cakewhiz.com/chocolate-date-balls/
https://detoxinista.com/raw-brownie-bites-vegan-paleo/

The most recent variation of these that I'm hooked on is made with:
medjool dates
crushed roasted pistachios
crushed roasted almonds
unsweetened cocoa powder
1 teaspoon vanilla extract
pinch of salt
ORANGE Zest
(tablespoon of water ONLY if needed!)

Blitz the ingredients in the food processor and until the mixture comes together (it should be wet but not too loose). Roll into balls or logs and then roll again in cocoa powder. Store in the freezer until ready to eat.

They are great throughout the day and provide an extra burst of energy and natural sweetness!