For calendar dates, please see day.
A date or rendezvous was a meeting of two individuals with a romantic intention.
Geoff Miles, a fourth grade student from Worley Elementary School, asked the question to the crew of Enterprise NX-01, "Is dating allowed on Enterprise?" to which Captain Jonathan Archer replied "Well, it's not discouraged, but there isn't a lot of privacy on a starship. Most of our crew share quarters with at least one other person, so it wouldn't exactly be practical. But if two crew members decide that they really like each other, there are a lot of places they can go to look at the stars." (ENT: "Breaking the Ice")
Jean-Luc Picard had a rendezvous with Jenice Manheim at the Café des Artistes in Paris, France in 2342 but ultimately didn't show up. (TNG: "We'll Always Have Paris")
In 2366, Geordi La Forge had a date with Christy Henshaw. Ultimately, she rejected him stating that she likes him platonically, not romantically. (TNG: "Booby Trap")
In 2374, Quark set up an one month anniversary of Odo's and Kira's first date so he could conduct some illicit business involving Denevan crystals with a Nausicaan. (DS9: "The Sound of Her Voice")
In 2375, Chakotay, while posing as Jason Hayek to infiltrate the training simulation on Terrasphere 8, used a tactical report due in the morning as an excuse to finish his date with "Valerie Archer". (VOY: "In the Flesh")
Seven of Nine brought a picnic basket to her third date with Chakotay. (VOY: "Endgame")