The primary application that has been discussed over the years has been with regards to mixed seating at weddings. See also Rabbi Eli Clark, "Mixed Seating at Weddings" (pdf), Journal of Halacha and Contemporary Society.
Rabbi Moshe Feinstein allowed it (OCI:41), based on Talmudic discussions related to seating at the Passover Seder.
His son-in-law, Rabbi Moshe Tendler, purposely had mixed tables for eligible singles and separate tables for everyone else at the weddings of all his children, which Rabbi Feinstein attended. Though some of Rabbi Feinstein's other children had different seating arrangements.
Kitzur Shulchan Aruch prohibits it.
A fantastic essay on the subject is available by Rabbi Yehuda Herzl Henkin; in English it appears in Responsa on Contemporary Jewish Issues Chapter 19, in Hebrew it's Bnei Banim I:35 and available on hebrewbooks.org. He eloquently argues that seating men and women in the same room, at separate tables, with no mechitza is more than satisfactory; and has mixed feelings about mixed tables. (I recall elsewhere in Bnei Banim he argues for supervised mixed singles events.) He argues that the verse in Zechariah quoted by many naysayers was only intended for prayer services, Torah-study sessions, and the like.
A few key quotes from the essay:
When sheva brachot were held at my grandfather's apartment [Rabbi Yosef Eliyahu Henkin, the primary Halachic decisor for America in the 1940s and 1950s], the organizers seated my wife in a corner outside the dining room with a handful of women. I protested ... the feast is called "the rejoicing of the groom and bride" ... [w]here is the rejoicing of the bride? My grandfather accepted my words but said that it is difficult to contest an established practice, but I think anyone who is able to should protest. ...
Still ... mingling of men and women should be forbidden at weddings where there is often kalut rosh [lightheadedness] ... Perhaps the community relies on the fact that drunkenness at weddings today is not common. [My comment: I wish...] ...
I have thus presented many reasons to exonerate the practice of mixed seating. Nonetheless, when it is not completely necessary one should not purify the impure. Hirhur [sinful thoughts] exists at many weddings today, especially among unmarried youths ... [f]or this reason it would be better to seat male and female teenagers separately, even if couples sit together.
He later added:
I retract what I wrote... that at weddings it is proper to seat single men and single women separately even if the married couples sit together. This is [still] so with young men and women who are not yet ready to get married. However, regarding those who have reached that stage, to the opposite, it is a mitzvah so that they get to know each other in a place where there is no concern for yihud and each couple is not alone on a "date," as is done today...